Question

Докажите неравенство (x+8)^2>x(x+16)​

Answer 1

(x+8)² = x² + 16x + 64

x(x+16) = x² + 16x

x² + 16x + 64 > x² + 16x

Answer 2

$(x + 8 {)}^{2} > x(x + 16) \\ {x}^{2} + 16x + 64 > {x}^{2} + 16x \\ 16x + 64 > 16x \\ 64 > 0$
Верно!