Question

If x= 3-√8,then(x-1/x)²= ____​

Answer 1

Answer:

32

Step-by-step explanation:

x = 3 - √8 thus 1/x = 1/(3 - √8)

Rationalize LHS :

=> 1/x = 1/(3 - √8) × (3 + √8)/(3 + √8)

=> 1/x = (3 + √8)/(3 - √8)(3 + √8)

=> 1/x = (3 + √8)/(3² - √8²)

=> 1/x = (3 + √8)/(9 - 8)

=> 1/x = 3 + √8

Therefore,

=> (x - 1/x)² = (3 - √8 - (3 + √8))²

=> (x - 1/x)² = (3 - √8 - 3 - √8)² = (-√8 - √8)²

=> (x - 1/x)² = (-2√8)² = 4×8 = 32

Answer 2

QUESTION:-

If $x=3-\sqrt{8}$,then $(x-\frac{1}{x}^2)=?$

EXPLANATION:-

$x=3-\sqrt{8}$   (GIVEN)

$\frac{1}{x}=\frac{1}{3-\sqrt{8}}$

$==>\frac{1}{3-\sqrt{8}}\\\\\\==>\frac{1}{3-\sqrt{8}}*\frac{3+\sqrt{8}}{3+\sqrt{8}}\\\\\\==>\frac{3+\sqrt{8}}{(3)^2-(\sqrt{8})^2} \\\\\==>\frac{3+\sqrt{8}}{9-8} \\\\\\\\==>\frac{3+\sqrt{8}}{1} \\\\\\==>\bold{\boxed {\frac{1}{x}=\frac{1}{3-\sqrt{8}}=\frac{3+\sqrt{8}}1}}$

Putting the value in the question we get:-

$(x-\frac{1}{x}^2)=[(3-\sqrt{8})-(3+\sqrt{8})]^2\\\\\\==>(x-\frac{1}{x}^2)=(3-\sqrt{8}-3-\sqrt{8})^2\\\\\\\==>(x-\frac{1}{x}^2)=(-\sqrt{8}-\sqrt{8}})^2\\\\\\==>(x-\frac{1}{x}^2)=(-2\sqrt{8})^2\\\\\\==>(x-\frac{1}{x}^2)=4*8\\\\\\==>(x-\frac{1}{x}^2)=32$

so (x-1/x)²=32