Question

if X=1/3-√2 then find the value of X square +1/X squaare​

Answer 1

EXPLANATION.

⇒ x = 1/(3 - √2).

As we know that,

We can write equation as,

⇒ 1/x = 1/1/(3 - √2).

⇒ 1/x = (3 - √2).

To find :

⇒ (x² + 1/x²).

First we rationalizes the value of x, we get.

⇒ x = 1/(3 - √2).

⇒ x = 1/(3 - √2) x (3 + √2)/(3 + √2).

⇒ x = (3 + √2)/[(3)² - (√2)²].

⇒ x = (3 + √2)/[9 - 2].

⇒ x = (3 + √2)/(7).

⇒ (x)² = [(3 + √2)/7]².

⇒ (x²) = [9 + 2 + 6√2/49].

⇒ (x)² = [11 + 6√2/49].

⇒ (1/x)² = (3 - √2)².

⇒ (1/x)² = 9 + 2 - 6√2.

⇒ (1/x)² = 11 - 6√2.

⇒ (x)² + (1/x)².

⇒ [11 + 6√2/49] + [11 - 6√2].

⇒ [11 + 6√2 + 49(11 - 6√2)/(49)].

⇒ [11 + 6√2 + 539 - 294√2]/(49).

⇒ [550 - 288√2]/(49).

Answer 2

Ans:- x = 1/(3-√2) × (3+√2)/(3+√2)

= (3+√2)/(9 - 2)

= (3+√2)/7

=> 1/x = 3-√2

now,

=> (x + 1/x)² = x²+1/x²+2×x×1/x

=> (3/7 + √2/7 + 3 - √2)² = x²+1/x²+2

=> ((3+√2+21-7√2)/7)² = x²+1/x²+2

=> (24/7-6√2/7)² = x²+1/x²+2

=> 441/7 + 72/49 - 288√2/7 = x²+1/x²+2

=> 441/7 + 72/49 - 288√2/7 - 2 = x²+1/x²

=> (441 + 72 - 288√2 - 98)/2 = x²+1/x²

=> (343+72-288√2)/2 = x² + 1/x²

=> 415/2 - 144√2 = x² + 1/x²

here is your answer

hope it will help you