Question

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

Answer 1

Answer:

4

Step-by-step explanation:

fx=1−2,find(x−x1)2.

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

x= 1-√2

Now find the value of 1/x.

\sf{\dfrac{1}{x}=\dfrac{1}{1-\sqrt{2}}}x1=1−21

\to\sf{\dfrac{1}{x}=\dfrac{1+\sqrt{2}}{(1-\sqrt{2})(1+\sqrt{2})}}→x1=(1−2)(1+2)1+2

\to\sf{\dfrac{1}{x}=\dfrac{1+\sqrt{2}}{-1}}→x1=−11+2

\to\sf{\dfrac{1}{x}=-(1+\sqrt{2})}→x1=−(1+2)

\to\sf{\dfrac{1}{x}=-1-\sqrt{2}}→x1=−1−2

Now find the value of \sf{(x-\dfrac{1}{x})^2}(x−x1)2

\begin{gathered} \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 \} \end{gathered}(x−x1)2→(1−2+1+2)2→(1+1)2→22→4{answer}

Answer 2

Answer:

Hope it helps you!!!!!!