Question

If x + 1/x = 6 find the value of (i) x^2 + 1/x^2 (ii) x^4 +1/ x^4​

Answer 1

(x+1/x) ^2=x^2+1/x^2+2×x×1/x

(6)^2=x^2+1/x^2+2

36-2=x^2+1/x^2

34=x^2+1/x^2

(x^2+1/x^2)=x^4+1/x^4+2×x^2×1/x^2

1156-2=x^4+1/x^4

1154=x^4+1/x^4

Answer 2

Answer:

$x^{2} + \frac{1}{x^{2}} = 34$

$x^{4} + \frac{1}{x^{4}} = 1154$

Step-by-step explanation:

$x + \frac{1}{x} = 6\\\\=> (x + \frac{1}{x})^{2} = 6^{2}\\\\=> x^{2} +\frac{1}{x^{2}} + 2*x*\frac{1}{x} = 36\\\\=> x^{2} + \frac{1}{x^{2}} = 36 - 2 = 34\\\\=> x^{2} + \frac{1}{x^{2}} = 34$

$x^{2} + \frac{1}{x^{2}} = 34\\\=> (x^{2} + \frac{1}{x^{2}})^{2} = 34^{2}\\\\=> x^{4} + \frac{1}{x^{4}} + 2*x^{2}*\frac{1}{x^{2}} = 1156\\\\=> x^{4} + \frac{1}{x^{4}} = 1156 - 2\\\\=> x^{4} + \frac{1}{x^{4}} = 1154$

Please brainlist my answer, if helpful!