Question

if x+1/x=8, then find x^4+1/x^4 , x^2+1/x^2? pls help

Answer 1

hey! here's your answer!
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Given :

x + $\frac{1}{x}$ = 8

we know that,

(a + b)² = a² + b² + 2ab

so, using the above Identity, we will solve !

(x + $\frac{1}{x}$)² = (x)² + ( $\frac{1}{x}$ )² + 2($\cancel{x}$)( $\frac{1}{\cancel{x}}$)

substituting the value of x + $\frac{1}{x}$ ,

(8)² = x² + $\frac{1}{{x}}^{2}$ + 2

=> 64 = x² + $\frac{1}{{x}}^{2}$ + 2

now, 2 is positive, and if we will take it to other side, it will become negative!

=> x² + $\frac{1}{{x}}^{2}$ = 64 - 2

=> x² + $\frac{1}{{x}}^{2}$ = 62

then, again squaring both sides,

=>( x² + $\frac{1}{{x}}^{2}$)² = (x² )² + ($\frac{1}{{x}}^{2}$)² + 2($\cancel{{x}}^{2}$)($\frac{1}{\cancel{{x}}^{2}}$)

=> (62)² = x⁴ + $\frac{1}{{x}}^{4}$ + 2

=> 3844 = x⁴ + $\frac{1}{{x}}^{4}$ + 2

=> x⁴ + $\frac{1}{{x}}^{4}$ = 3844 - 2

=> x⁴ + $\frac{1}{{x}}^{4}$ = 3842 .....answer!