Question

6(2x+1)^2 +1-12x(x+3)=4(2x-1)^2

Answer 1

Ответ:

$-\frac{1}{2};\ 1\frac{1}{2}$

Объяснение:

$6(2x+1)^2+1-12x(x+3)=4(2x-1)^2\\\\6(4x^2+4x+1)+1-12x^2-36x=4(4x^2-4x+1)\\\\24x^2+24x+6+1-12x^2-36x=16x^2-16x+4\\\\24x^2+24x+6+1-12x^2-36x-16x^2+16x-4=0\\\\-4x^{2}+4x+3=0\\\\ a=-4,\ b=4,\ c=3\\\\D=b^2-4ac=4^2-4\cdot(-4)\cdot3=16+48=64\\\\\sqrt{D}=\sqrt{64}=8\\\\x_1=\frac{-b-\sqrt{D}}{2a}=\frac{-4-8}{2\cdot(-4)}=\frac{-12}{-8}=\frac{3}{2}=1\frac{1}{2}\\\\x_2=\frac{-b+\sqrt{D}}{2a}=\frac{-4+8}{2\cdot(-4)}=\frac{4}{-8}=-\frac{1}{2}$