Question

If x=1-root2find the value of x+1/x

Answer 1

Given :-

x = 1 - √2

Therefore 1/x = 1/(1 - √2)

By rationalizing, we get

= 1/(1 - √2) × (1 + √2)/(1 + √2)

= (1 + √2)/[(1 - √2)(1 + √2)]

= (1 + √2)/[(1)² - (√2)²]

= (1 + √2)/(1 - 2)

= (1 + √2)/-1

= -(1 + √2)

= -1 - √2

Hence, the value of x + 1/x :-

= 1 - √2 + (-1 - √2)

= 1 - √2 - 1 - √2

= -2√2 Final Answer!

Identity used :-

(a + b)² = a² + 2ab + b²

Proof :-

= (a + b)(a + b)

= a(a + b) + b(a + b)

= a² + ab + ab + b²

= a² + 2ab + b²

Answer 2

Step-by-step explanation:

Given :-

Given :-x = 1 - √2

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!Identity used :-

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!Identity used :-(a + b)² = a² + 2ab + b²

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!Identity used :-(a + b)² = a² + 2ab + b²Proof :-

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!Identity used :-(a + b)² = a² + 2ab + b²Proof :-= (a + b)(a + b)

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!Identity used :-(a + b)² = a² + 2ab + b²Proof :-= (a + b)(a + b)= a(a + b) + b(a + b)

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!Identity used :-(a + b)² = a² + 2ab + b²Proof :-= (a + b)(a + b)= a(a + b) + b(a + b)= a² + ab + ab + b²

Given :-x = 1 - √2Therefore 1/x = 1/(1 - √2)By rationalizing, we get= 1/(1 - √2) × (1 + √2)/(1 + √2)= (1 + √2)/[(1 - √2)(1 + √2)]= (1 + √2)/[(1)² - (√2)²]= (1 + √2)/(1 - 2)= (1 + √2)/-1= -(1 + √2)= -1 - √2Hence, the value of x + 1/x :-= 1 - √2 + (-1 - √2)= 1 - √2 - 1 - √2= -2√2 Final Answer!Identity used :-(a + b)² = a² + 2ab + b²Proof :-= (a + b)(a + b)= a(a + b) + b(a + b)= a² + ab + ab + b²= a² + 2ab + b²