M=(2x-1)^2-(x+3)^2 eching

$$M = ( 2 x - 1 ) ^ { 2 } - ( x + 3 ) ^ { 2 }$$

M uchun yechish

$$M=\left(x-4\right)\left(3x+2\right)$$

Yechim qadamlari

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

$$M=4x^{2}-4x+1-\left(x+3\right)^{2}$$

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

$$M=4x^{2}-4x+1-\left(x^{2}+6x+9\right)$$

x^{2}+6x+9 teskarisini topish uchun har birining teskarisini toping.

$$M=4x^{2}-4x+1-x^{2}-6x-9$$

3x^{2} ni olish uchun 4x^{2} va -x^{2} ni birlashtirish.

$$M=3x^{2}-4x+1-6x-9$$

-10x ni olish uchun -4x va -6x ni birlashtirish.

$$M=3x^{2}-10x+1-9$$

-8 olish uchun 1 dan 9 ni ayirish.

$$M=3x^{2}-10x-8$$

x uchun yechish (complex solution)

$$x=\frac{-\sqrt{3M+49}+5}{3}$$

$$x=\frac{\sqrt{3M+49}+5}{3}$$

x uchun yechish

$$x=\frac{-\sqrt{3M+49}+5}{3}$$

$$x=\frac{\sqrt{3M+49}+5}{3}\text{, }M\geq -\frac{49}{3}$$