# Find the value of the given equation:

x + 1/x =3, then the value of x^{5} + 1/x^{5} is

- 132
- 122
- 123
- 110

**Answer is 123 **

**Explanation:-**X + 1/X = 3

Square on both side,

(X + 1/X)

^{2}= 3

^{2}

X

^{2 }+ 1/X

^{2}+ 2 X x 1/X = 9

X

^{2 }+ 1/X

^{2}+ 2 = 9

X

^{2 }+ 1/X

^{2}= 9 – 2

X

^{2 }+ 1/X

^{2}= 7 ………………………(1)

Again, X + 1/X = 3

Cube on both side,

(X + 1/X)^{3} = 3^{3}

X^{3} + 1/X^{3} + 3 x X x 1/X (X + 1/X) = 3 x 3 x 3

X^{3} + 1/X^{3} + 3 x 3 = 27

X^{3} + 1/X^{3} = 27 – 9

X^{3} + 1/X^{3} = 18 …………………. (2)

Equation (1) multiply by (2),

(X^{2 } + 1/X^{2}) (X^{3} + 1/X^{3}) = 7 x 18

X^{2} x X^{3} + X^{2} x 1/X^{3} + X^{3} x 1/X^{2} + 1/X^{2} x X^{3} = 126

X^{5} + 1/X + X + 1/X^{5} = 126

X^{5} + 1/X^{5} + X + 1/X = 126

X^{5} + 1/X^{5} + 3 = 126

X^{5} + 1/X^{5} = 126 – 3

X^{5} + 1/X^{5} = 123

Then, the value of X^{5} + 1/X^{5} is 123.

Hence, the correct answer is option (3) 123.