Question

if 3-2√2 find x²+1/x²​

Answer 1

Answer :

x² + 1/x² = 34

Solution :

• Given : x = 3 - 2√2
• To find : x² + 1/x²

We have ;

x = 3 - 2√2

Then ,

1/x = 1/(3 - 2√2)

Now ,

Rationalising the denominator of the term in RHS , we have ;

=> 1/x = (3 + 2√2) / (3 - 2√2)(3 + 2√2)

=> 1/x = (3 + 2√2) / [ 3² - (2√2)² ]

=> 1/x = (3 + 2√2) / (9 - 8)

=> 1/x = (3 + 2√2) / 1

=> 1/x = 3 + 2√2

Now ,

We know that ,

(a + b)² = a² + b² + 2ab

Thus ,

=> (x + 1/x)² = x² + (1/x)² + 2•x•(1/x)

=> (3 - 2√2 + 3 + 2√2)² = x² + 1/x² + 2

=> 6² = x² + 1/x² + 2

=> 36 = x² + 1/x² + 2

=> x² + 1/x² = 36 - 2

=> x² + 1/x² = 34

Hence , x² + 1/x² = 34 .