Question

If x^2+1/x^2=79 , then find value of x+1/X

Answer 1

(x+1/x)^2=x^2+1/x^2+2x×1/x
(x+1/x)^2=79+2
x+1/x=√81
x+1/x=+-9
is your answer

Answer 2

$(x + \frac{1}{x} ) {}^{2} \\ = x {}^{2} + \frac{1}{x {}^{2} } + 2 \times x \times \frac{1}{x} \\ = x { }^{2} + \frac{1}{x { }^{2} } + 2 \\ \\ it \: is \: given \: that \: x {}^{2} + \frac{1}{x {}^{2} } = 79 \\ so \\ = 79 + 2 = 81 \\ (x + \frac{1}{x} ) {}^{2} = 81 \\ x + \frac{1}{x} = \sqrt{81} = 9$