E=left(3x-2right)^2-left(x+1right)^2 eching

$$E = { \left(3x-2 \right) }^{ 2 } - { \left(x+1 \right) }^{ 2 }$$

E uchun yechish

$$E=\left(2x-3\right)\left(4x-1\right)$$

Yechim qadamlari

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(3x-2\right)^{2} kengaytirilishi uchun ishlating.

$$E=9x^{2}-12x+4-\left(x+1\right)^{2}$$

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(x+1\right)^{2} kengaytirilishi uchun ishlating.

$$E=9x^{2}-12x+4-\left(x^{2}+2x+1\right)$$

x^{2}+2x+1 teskarisini topish uchun har birining teskarisini toping.

$$E=9x^{2}-12x+4-x^{2}-2x-1$$

8x^{2} ni olish uchun 9x^{2} va -x^{2} ni birlashtirish.

$$E=8x^{2}-12x+4-2x-1$$

-14x ni olish uchun -12x va -2x ni birlashtirish.

$$E=8x^{2}-14x+4-1$$

3 olish uchun 4 dan 1 ni ayirish.

$$E=8x^{2}-14x+3$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{8E+25}+7}{8}$$

$$x=\frac{\sqrt{8E+25}+7}{8}$$

x uchun yechish

$$x=\frac{-\sqrt{8E+25}+7}{8}$$

$$x=\frac{\sqrt{8E+25}+7}{8}\text{, }E\geq -\frac{25}{8}$$