Question

If x =1-√2 then find the value of (x-1/x)²​

Answer 1

Answer:

4

Step-by-step explanation:

Given x = 1 - √2

$\implies \sf{ \dfrac{1}{x} = \dfrac{1}{1-\sqrt2}}$

Rationalising the denominator(multiply and divide by 1 + √2)

$\implies \sf{\dfrac{1}{x} = \dfrac{1}{1+\sqrt{2}} \times\dfrac{1+\sqrt{2}}{1+\sqrt{2}}}\\\\\implies\sf{ \dfrac{1}{x} = \dfrac{1+\sqrt{2}}{(1-\sqrt{2})(1+\sqrt{2})}}\\\\\implies\sf{\dfrac{1}{x} =\dfrac{1+\sqrt{2}}{1^2-(\sqrt{2})^2}} = \dfrac{1+\sqrt{2}}{1-2}\\\\\implies\sf{\dfrac{1}{x} =\dfrac{1+\sqrt2}{-1}=-1-\sqrt2}$

Hence,

x - 1/x = (1 - √2) - (-1 - √2) = 2

Hence,

(x - 1/x)² = 2² = 4

Answer 2

Answer:

Hope it helps you!!!!!!!