Question

(x-5)(2x-5)-(2x-7)la puterea 2 < 2(1-x2)

Answer 1

$\displaystyle \\ x(x-5)(2x-5)-(2x-7)^2\ \textless \ 2(1-x^2) \\ 2x^2-5x-10x+25-[(2x)^2-2 \cdot 2x \cdot 7+7^2]\ \textless \ 2-2x^2 \\ 2x^2-5x-10x+25-(4x^2-28x+49)\ \textless \ 2-2x^2 \\ 2x^2-5x-10x+25-4x^2+28x-49\ \textless \ 2-2x^2 \\ 2x^2-5x-10x-4x^2+28x+2x^2\ \textless \ 2-25+49 \\ 13x\ \textless \ 26 \\ x\ \textless \ \frac{26}{13} \\ x\ \textless \ 2$