Question

if x-1/x =3√2 find the value of x square + 1/xsquare​

Answer 1

Question:

If x - 1/x = 3√2 , then find the value of

x^2 + 1/x^2.

Note:

• (a + b)^2 = a^2 + b^2 + 2•a•b
• (a - b)^2 = a^2 + b^2 - 2•a•b
• a^2 - b^2 = (a + b)(a - b)

Solution;

We have;

x - 1/x = 3√2 -----------(1)

Also,

We know that;

(a - b)^2 = a^2 + b^2 - 2•a•b

Thus;

=> (x - 1/x)^2 = x^2 + 1/x^2 - 2•x•(1/x)

=> (3√2)^2 = x^2 + 1/x^2 - 2

=> 18 = x^2 + 1/x^2 - 2 {using eq-(1)}

=> x^2 + 1/x^2 = 18 + 2

=> x^2 + 1/x^2 = 20

Hence,

The required value of x^2 + 1/x^2 = 20.