Question

if[x+1/x]=4, then the value of [x2 + 1/x2]is

Answer 1

Answer:

=4

Step-by-step explanation:

x+x1=4        

Squaring (1) in both sides, we get

(x+\dfrac{1}{x})^{2}=4^{2}(x+x1)2=42

⇒ x^2+\dfrac{1}{x^2}+2.x.\dfrac{1}{x} =16x2+x21+2.x.x1=16

⇒ x^2+\dfrac{1}{x^2}+2 =16x2+x21+2=16

⇒x^2+\dfrac{1}{x^2}=16-2=14x2+x21=16−2=14

∴ x^2+\dfrac{1}{x^2}=14x2+x21=14

Hence, x^2+\dfrac{1}{x^2}=14x2+x21=14