Question

EU SEI A ALTERNATIVA SO QUERO O PASSO A PASSO Se (1,2)$(1,2)^{-1/2} = x$, quanto vale $x^{2} + 1?$?


(A) 1

(B) 11/6

(C) 6/11

(D) 10/3

(E) -11/6

Answer 1

Explicação passo-a-passo:

Seja $\sf k=x^2+1$

$\sf (1,2)^{\frac{-1}{2}}=x$

$\sf x=(1,2)^{\frac{-1}{2}}$

$\sf x=\Big(\dfrac{12}{10}\Big)^{\frac{-1}{2}}$

$\sf x=\Big(\dfrac{6}{5}\Big)^{\frac{-1}{2}}$

$\sf x=\Big(\dfrac{5}{6}\Big)^{\frac{1}{2}}$

Logo:

$\sf k=\Big[\Big(\dfrac{5}{6}\Big)^{\frac{1}{2}}\Big]^2+1$

$\sf k=\Big(\dfrac{5}{6}\Big)^{\frac{1\cdot2}{2}}+1$

$\sf k=\Big(\dfrac{5}{6}\Big)^{\frac{2}{2}}+1$

$\sf k=\Big(\dfrac{5}{6}\Big)^{1}+1$

$\sf k=\dfrac{5}{6}+1$

$\sf k=\dfrac{5+6}{6}$

$\sf \red{k=\dfrac{11}{6}}$

Letra B