Question

Dados x= raiz quadrada de 1,777... e y=0,333... qual é o valor de (x-y) elevado a -2

Answer 1

$m=1,777...\times(10)\\10m=17,777....$

$\underline{\begin{cases}10m=17,\cancel{777...} \\m=1,\cancel{777...}\end{cases}}$

$9m=16\\m=\dfrac{16}{9}$

$x=\sqrt{1,777}\\x=\sqrt{\dfrac{16}{9}}=\dfrac{4}{3}$

$y=0,333\times(10)\\10y=3,333...$

$\underline{\begin{cases}10y=3,\cancel{333...} \\y=0,\cancel{333...}\end{cases}}$

$9y=3\\y=\dfrac{3\div3}{9\div3}\\y=\dfrac{1}{3}$

$x-y=\dfrac{4}{3}-\dfrac{1}{3}=\dfrac{3}{3}=1$

$\boxed{\boxed{\mathsf{{(x-y)}^{-2}={1}^{-2}=1}}}$