Question

evaluate x^2+1/x^2 when x=3+√8​

Answer 1

x=3+√8

therfore 1/x= 1/(3+√8)

rationalizing it we get (3-√8)

there fore x^2 + 1/x^2 = (3+√8)^2 + (3-√8)^2

= 9 + 6√8 + 8+( 9 - 6√8 + 8)

= 9+9+8+8

= 34.

Answer 2

$\huge\text{\underline{Answer}}$

We have

$x = 3 + \sqrt{8}$

and

$\frac{1}{x} = 3 - \sqrt{8}$

Now by using suitable identity.

★ $\boxed{\sf{ (a + b) ^{2} = {a}^{2} + {b}^{2} + 2ab}}$

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

put the value,

$\implies$ $(3 + \sqrt{8} + 3 - \sqrt{8} ) ^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

$\implies$ ${6}^{2} - 2 = {x}^{2} + \frac{1}{ {x}^{2} }$

$\implies$ $36 - 2 = {x}^{2} + \frac{1}{ {x}^{2} }$

$\implies$ ${x}^{2} + \frac{1}{ {x}^{2} } = 34$