Question

Sendo A=(x+1/x)² e B=(x-1/x)² , Calcule (A-B)²

Answer 1

Resposta:

A=(x+1/x)² e B=(x-1/x)²

A=x²+2*x*(1/x)+1/x²=x²+2+1/x²

B=x²-2*x*(1/x)+1/x²=x²-2+1/x²

(A -B) =x²+2+1/x² - [x²-2+1/x²]

(A-B) =2+2=4

(A-B)²= 4² = 16

Answer 2

Resposta:   16

Explicação passo-a-passo:

$A=(x+\frac{1}{x})^2  \  e \ B=(x-\frac{1}{x})^2\\\\(A-B)^2=\left[(x+\frac{1}{x})^2-(x-\frac{1}{x})^2\right]^2\\\\(A-B)^2=\left[x^2+2x.\frac{1}{x}+\frac{1}{x^2}-(x^2-2x.\frac{1}{x}+\frac{1}{x^2})\right]^2\\\\(A-B)^2=\left[x^2+2+\frac{1}{x^2}-x^2+2-\frac{1}{x^2})\right]^2\\\\(A-B)^2=\left[4]^2=16$