Question

x + 1/x = 5 then find the value of x^2 + 1/x^2​

Answer 1

Answer:

Value of x² + 1/x² is 23.

Step-by-step explanation:

x + 1/x = 5

Squaring on both sides

( x + 1/x )² = 5²

Using algebraic identity ( a + b )² = a² + b² + 2ab

x² + ( 1/x )² + 2( x )( 1/x ) = 25

x² + 1/x² + 2 = 25

x² + 1/x² = 25 - 2 = 23

Therefore the value of x² + 1/x² is 23.

Answer 2

Answer:x² + $\frac{1}{x^2}$ = 23

Step-by-step explanation:  x + $\frac{1}{x}$ = 5 and we have to find x² + $\frac{1}{x^2}$

so :

x + $\frac{1}{x}$  =  5

NOW WE WILL SQUARE BOTH SIDES

( x + $\frac{1}{x}$)² = 5²

{(a + b)² = a² + 2ab + b²}

Hence using this identity here

x² + 2(x)($\frac{1}{x}$) + $\frac{1}{x^2}$ =  25

= x² + 2  +  $\frac{1}{x^2}$  = 25

= x² + $\frac{1}{x^2}$ = 25 - 2

= x² + $\frac{1}{x^2}$ = 23

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