Question

to no 7o ano, ex 6 da foto em anexo

Answer 1

Olá, Heisenberg.

$BC = AB - AC = 10 - x\\\\ AC\²=AB \cdot BC \Rightarrow\\\\ x\² = 10 \cdot (10 - x) \Rightarrow\\\\ x\² = 100 - 10x \Rightarrow\\\\ x\² + 10x - 100 = 0 \Rightarrow\\\\ \Delta = 10\² + 4\cdot100 = 100 + 400 = 500 \Rightarrow\\\\ \sqrt\Delta = \sqrt{500} = \sqrt{5\cdot100}=10\sqrt5=10\cdot2,23=22,3 \Rightarrow\\\\ x=\frac{-10\pm22,3}{2}=\text{(desprezando-se a raiz negativa)}\frac{-10+22,3}2=6,15\\\\ \therefore\boxed{x = 6,15}$