If $(x + \frac{2}{x})= 7$, then what is the value of $(2x^2 + \frac{8}{x^2})$ ?

90

If $(x + \frac{2}{x})= 7$,

then what is the value of $(2x^2 + \frac{8}{x^2})$ = ?

we know that,

If $K+\frac{1}{K}=n$

then, $K^2+\frac{1}{K^2}$ = n² – 2 × k × \(\frac{1}{k}\)

If $(x + \frac{2}{x})= 7$,

then, If $(x^2 + \frac{4}{x^2})$ = 7² – 2 × 1 × \(\frac{2}{x}\) = 49 - 4 = 45

multiply the above equation by 2 to get the desired equation,

$(2x^2 + \frac{8}{x^2})$ = 45 × 2 = 90