Question

Efectuati: (3x-4)^2-(2x-3)^2+24=5(x+1)^2-18

Answer 1

$\displaystyle (3x-4)^2-(2x-3)^2+24=5(x+1)^2-18 \\ (3x)^2-2 \cdot 3x \cdot 4+4^2-[(2x)^2-2 \cdot 2x \cdot 3+3^2]+24=5(x+1)^2-18 \\ 9x^2-24x+16-(4x^2-12x+9)+24=5(x^2+2 \cdot x \cdot 1+1^2)-18 \\ 9x^2-24x+16-4x^2+12x-9+24=5(x^2+2x+1)-18 \\ 9x^2-24x+16-4x^2+12x-9+24=5x^2+10x+5-18 \\ 9x^2-4x^2-5x^2-24x+12x-10x=5-18-16+9-24 \\ -22x=-44 \Rightarrow x= \frac{-44}{-22} \Rightarrow x=2$