Question

if X2+1/X2=7 then find x+1/x​

Answer 1

Given,

The value of x²+1/x² = 7

To Find,

The value of x+1/x

Solution,

Since we are given the value of x²+1/x² = 7

Now,

(x+1/x)² = x² + 1/x² + 2

(x+1/x)² = 7 + 2

(x+1/x)² = 9

x+1/x = 3

Hence, the value of x+1/x = 3.

Answer 2

We know the formula: $(a+b)^{2} = a^{2} +b^{2} + 2ab$

Here given the equation:

$\frac{x^{2}+1 }{x^{2} } =7$ .......(i)

we have to find the value of $\frac{x+1}{x}$

For that apply squaring, we get:

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

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

$(1+\frac{1}{x} )^{2} = 7+2$ from equation (i)

$(1+\frac{1}{x} )^{2} = 9$

$1+\frac{1}{x} = 3$

Therefore the value of $x+\frac{1}{x} = 3.$