Question

if x = 1 - √2 find ( x - 1/x)²​

Answer 1

Answer:

x=1-√2

1/x= 1/1-√2

rationalize it

1/x= -1-√2

now

{(1-√2-(-1-√2)}^2

(1-√2+1+√2)^2

2^2= 4

Step-by-step explanation:

please mark brainliest and thank

Answer 2

★${\underline{\underline{\large{\bold{Question:-}}}}}$

$\sf{If\:x=1-\sqrt{2},\:find\:(x-\dfrac{1}{x})^2.}$

★ ${\underline{\underline{\large{\bold{Solution:-}}}}}$

x= 1-√2

Now find the value of 1/x.

$\sf{\dfrac{1}{x}=\dfrac{1}{1-\sqrt{2}}}$

$\to\sf{\dfrac{1}{x}=\dfrac{1+\sqrt{2}}{(1-\sqrt{2})(1+\sqrt{2})}}$

$\to\sf{\dfrac{1}{x}=\dfrac{1+\sqrt{2}}{-1}}$

$\to\sf{\dfrac{1}{x}=-(1+\sqrt{2})}$

$\to\sf{\dfrac{1}{x}=-1-\sqrt{2}}$

Now find the value of $\sf{(x-\dfrac{1}{x})^2}$

$\sf \: {(x - \dfrac{1}{x} )}^{2} \\ \\ \to \sf \:(1 - \sqrt{2} + 1 + \sqrt{2} )^{2} \\ \\ \to \sf \: {(1 + 1)}^{2} \\ \\ \to \sf \: {2}^{2} \\ \\ \to \sf \: 4 \: \{answer \}$