Question

if x=3-2 root 2 then find (x-1/x)^3

Answer 1

Answer:

→ -128√2 .

Step-by-step explanation:

Given :-

→ x = 3 - 2√2 .

Then, 1/x = 1/(3 - 2√2 ) .

= 1/( 3 - 2√2 ) × ( 3 + 2√2 )/( 3 + 2√2 ) .

= ( 3 + 2√2 )/( 3² - (2√2)² ) .

= 3 + 2√2 .

Therefore, ( x - 1/x )³

= ( 3 - 2√2 - 3 - 2√2 ) ³ .

= ( -4√2 )³ .

= - 128√2 .

✔✔ Hence, it is solved ✅✅.

THANKS

Answer 2

$\bf \left( {x - \frac{1}{x} } \right)^{3} = - 128 \sqrt{2}$

Step-by-step explanation:

Given:

• $x = 3 - 2 \sqrt{2}$

To find:

• Find the value of $\left({x - \frac{1}{x} }\right)^{3}$

Solution:

Concept to be used:

• Rationalize the denominator for 1/x.
• Simply the expression.

Step 1:

Simplify 1/x.

$\frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} } \times \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} }$

or

$\frac{1}{x} = \frac{3 + 2 \sqrt{2} }{( {3)}^{2} - (2 \sqrt{2}) ^{2} }$

or

$\frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 8}$

or

$\bf \frac{1}{x} = 3 + 2 \sqrt{2}$

Step 2:

Simplify $\left(x - \frac{1}{x}\right )$.

$x - \frac{1}{x} = 3 - 2 \sqrt{2} - 3 - 2 \sqrt{2}$

or

$\bf x - \frac{1}{x} = - 4 \sqrt{2}...eq1$

Step 3:

Calculate $\left({x - \frac{1}{x} }\right)^{3}$

Take cube of eq1.

$( {x - \frac{1}{x} })^{3} = {( - 4 \sqrt{2}) }^{3}$

or

$\left( {x - \frac{1}{x} } \right)^{3} = - 128 \sqrt{2}$

Thus,

$\bf \left( {x - \frac{1}{x} } \right)^{3} = - 128 \sqrt{2}$

Learn more:

1) if x = 3 + √8. find the value of x^2 + 1/x^2

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2) if x-1/x=8 find x3-1/x3

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