(x-(-6-i))(x-(-6+i))(x-(-1+3i))(x-(-1+3i)) ಪರಿಹರಿಸಿ

$$( x - ( - 6 - i ) ) ( x - ( - 6 + i ) ) ( x - ( - 1 + 3 i ) ) ( x - ( - 1 + 3 i ) )$$

ಮೌಲ್ಯಮಾಪನ

$$\left(x+\left(6-i\right)\right)\left(x+\left(6+i\right)\right)\left(x+\left(1-3i\right)\right)^{2}$$

ಪರಿಹಾರ ಕ್ರಮಗಳು

\left(x-\left(-1+3i\right)\right)^{2} ಪಡೆದುಕೊಳ್ಳಲು x-\left(-1+3i\right) ಮತ್ತು x-\left(-1+3i\right) ಗುಣಿಸಿ.

$$\left(x-\left(-6-i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

-6-i ನ ವಿಲೋಮವು 6+i ಆಗಿದೆ.

$$\left(x+\left(6+i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

x-\left(-6+i\right) ದಿಂದ x+\left(6+i\right) ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$\left(x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(x-\left(-1+3i\right)\right)^{2} ದಿಂದ x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right) ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$x\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

6-i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -6+i ಗುಣಿಸಿ.

$$x\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

1-3i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -1+3i ಗುಣಿಸಿ.

$$x\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(x+\left(1-3i\right)\right)^{2} ವಿಸ್ತರಿಸಲು ಬೈನಾಮಿಯಲ್ ಪ್ರಮೇಯ \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ಬಳಸಿ.

$$x\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

x+\left(6-i\right) ದಿಂದ x ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$\left(x^{2}+\left(6-i\right)x\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

x^{2}+\left(6-i\right)x ನ ಪ್ರತಿ ಪದವನ್ನು x^{2}+\left(2-6i\right)x+\left(-8-6i\right) ನ ಪ್ರತಿ ಪದದೊಂದಿಗೆ ಗುಣಾಕಾರ ಮಾಡುವ ಮೂಲಕ ವಿಭಾಜಕ ಗುಣವನ್ನು ಅನ್ವಯಿಸಿ.

$$x^{4}+\left(2-6i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-i\right)x^{3}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(8-7i\right)x^{3} ಪಡೆದುಕೊಳ್ಳಲು \left(2-6i\right)x^{3} ಮತ್ತು \left(6-i\right)x^{3} ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(-2-44i\right)x^{2} ಪಡೆದುಕೊಳ್ಳಲು \left(-8-6i\right)x^{2} ಮತ್ತು \left(6-38i\right)x^{2} ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

6-i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -6+i ಗುಣಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

1-3i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -1+3i ಗುಣಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}$$

\left(x+\left(1-3i\right)\right)^{2} ವಿಸ್ತರಿಸಲು ಬೈನಾಮಿಯಲ್ ಪ್ರಮೇಯ \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ಬಳಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

x+\left(6-i\right) ದಿಂದ 6+i ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(\left(6+i\right)x+37\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

\left(6+i\right)x+37 ನ ಪ್ರತಿ ಪದವನ್ನು x^{2}+\left(2-6i\right)x+\left(-8-6i\right) ನ ಪ್ರತಿ ಪದದೊಂದಿಗೆ ಗುಣಾಕಾರ ಮಾಡುವ ಮೂಲಕ ವಿಭಾಜಕ ಗುಣವನ್ನು ಅನ್ವಯಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(18-34i\right)x^{2}+\left(-42-44i\right)x+37x^{2}+\left(74-222i\right)x+\left(-296-222i\right)$$

\left(55-34i\right)x^{2} ಪಡೆದುಕೊಳ್ಳಲು \left(18-34i\right)x^{2} ಮತ್ತು 37x^{2} ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(-42-44i\right)x+\left(74-222i\right)x+\left(-296-222i\right)$$

\left(32-266i\right)x ಪಡೆದುಕೊಳ್ಳಲು \left(-42-44i\right)x ಮತ್ತು \left(74-222i\right)x ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

\left(14-6i\right)x^{3} ಪಡೆದುಕೊಳ್ಳಲು \left(8-7i\right)x^{3} ಮತ್ತು \left(6+i\right)x^{3} ಕೂಡಿಸಿ.

$$x^{4}+\left(14-6i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

\left(53-78i\right)x^{2} ಪಡೆದುಕೊಳ್ಳಲು \left(-2-44i\right)x^{2} ಮತ್ತು \left(55-34i\right)x^{2} ಕೂಡಿಸಿ.

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-54-28i\right)x+\left(32-266i\right)x+\left(-296-222i\right)$$

\left(-22-294i\right)x ಪಡೆದುಕೊಳ್ಳಲು \left(-54-28i\right)x ಮತ್ತು \left(32-266i\right)x ಕೂಡಿಸಿ.

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-22-294i\right)x+\left(-296-222i\right)$$

ವಿಸ್ತರಿಸು

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-22-294i\right)x+\left(-296-222i\right)$$

ಪರಿಹಾರ ಕ್ರಮಗಳು

\left(x-\left(-1+3i\right)\right)^{2} ಪಡೆದುಕೊಳ್ಳಲು x-\left(-1+3i\right) ಮತ್ತು x-\left(-1+3i\right) ಗುಣಿಸಿ.

$$\left(x-\left(-6-i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

-6-i ನ ವಿಲೋಮವು 6+i ಆಗಿದೆ.

$$\left(x+\left(6+i\right)\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

x-\left(-6+i\right) ದಿಂದ x+\left(6+i\right) ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$\left(x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(x-\left(-1+3i\right)\right)^{2} ದಿಂದ x\left(x-\left(-6+i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right) ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$x\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

6-i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -6+i ಗುಣಿಸಿ.

$$x\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

1-3i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -1+3i ಗುಣಿಸಿ.

$$x\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(x+\left(1-3i\right)\right)^{2} ವಿಸ್ತರಿಸಲು ಬೈನಾಮಿಯಲ್ ಪ್ರಮೇಯ \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ಬಳಸಿ.

$$x\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

x+\left(6-i\right) ದಿಂದ x ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$\left(x^{2}+\left(6-i\right)x\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

x^{2}+\left(6-i\right)x ನ ಪ್ರತಿ ಪದವನ್ನು x^{2}+\left(2-6i\right)x+\left(-8-6i\right) ನ ಪ್ರತಿ ಪದದೊಂದಿಗೆ ಗುಣಾಕಾರ ಮಾಡುವ ಮೂಲಕ ವಿಭಾಜಕ ಗುಣವನ್ನು ಅನ್ವಯಿಸಿ.

$$x^{4}+\left(2-6i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-i\right)x^{3}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(8-7i\right)x^{3} ಪಡೆದುಕೊಳ್ಳಲು \left(2-6i\right)x^{3} ಮತ್ತು \left(6-i\right)x^{3} ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-8-6i\right)x^{2}+\left(6-38i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

\left(-2-44i\right)x^{2} ಪಡೆದುಕೊಳ್ಳಲು \left(-8-6i\right)x^{2} ಮತ್ತು \left(6-38i\right)x^{2} ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x-\left(-6+i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

6-i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -6+i ಗುಣಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x-\left(-1+3i\right)\right)^{2}$$

1-3i ಪಡೆದುಕೊಳ್ಳಲು -1 ಮತ್ತು -1+3i ಗುಣಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x+\left(1-3i\right)\right)^{2}$$

\left(x+\left(1-3i\right)\right)^{2} ವಿಸ್ತರಿಸಲು ಬೈನಾಮಿಯಲ್ ಪ್ರಮೇಯ \left(a+b\right)^{2}=a^{2}+2ab+b^{2} ಬಳಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)\left(x+\left(6-i\right)\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

x+\left(6-i\right) ದಿಂದ 6+i ಗುಣಿಸಲು ವಿಭಾಜಕ ಗುಣವನ್ನು ಬಳಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(\left(6+i\right)x+37\right)\left(x^{2}+\left(2-6i\right)x+\left(-8-6i\right)\right)$$

\left(6+i\right)x+37 ನ ಪ್ರತಿ ಪದವನ್ನು x^{2}+\left(2-6i\right)x+\left(-8-6i\right) ನ ಪ್ರತಿ ಪದದೊಂದಿಗೆ ಗುಣಾಕಾರ ಮಾಡುವ ಮೂಲಕ ವಿಭಾಜಕ ಗುಣವನ್ನು ಅನ್ವಯಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(18-34i\right)x^{2}+\left(-42-44i\right)x+37x^{2}+\left(74-222i\right)x+\left(-296-222i\right)$$

\left(55-34i\right)x^{2} ಪಡೆದುಕೊಳ್ಳಲು \left(18-34i\right)x^{2} ಮತ್ತು 37x^{2} ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(-42-44i\right)x+\left(74-222i\right)x+\left(-296-222i\right)$$

\left(32-266i\right)x ಪಡೆದುಕೊಳ್ಳಲು \left(-42-44i\right)x ಮತ್ತು \left(74-222i\right)x ಕೂಡಿಸಿ.

$$x^{4}+\left(8-7i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(6+i\right)x^{3}+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

\left(14-6i\right)x^{3} ಪಡೆದುಕೊಳ್ಳಲು \left(8-7i\right)x^{3} ಮತ್ತು \left(6+i\right)x^{3} ಕೂಡಿಸಿ.

$$x^{4}+\left(14-6i\right)x^{3}+\left(-2-44i\right)x^{2}+\left(-54-28i\right)x+\left(55-34i\right)x^{2}+\left(32-266i\right)x+\left(-296-222i\right)$$

\left(53-78i\right)x^{2} ಪಡೆದುಕೊಳ್ಳಲು \left(-2-44i\right)x^{2} ಮತ್ತು \left(55-34i\right)x^{2} ಕೂಡಿಸಿ.

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-54-28i\right)x+\left(32-266i\right)x+\left(-296-222i\right)$$

\left(-22-294i\right)x ಪಡೆದುಕೊಳ್ಳಲು \left(-54-28i\right)x ಮತ್ತು \left(32-266i\right)x ಕೂಡಿಸಿ.

$$x^{4}+\left(14-6i\right)x^{3}+\left(53-78i\right)x^{2}+\left(-22-294i\right)x+\left(-296-222i\right)$$