If x - -2 - -3-then-x3 - 1-x3- 4892

The correct option is A 4 x = (2 + √(3))^1/3⇒ x^3 = 2 + √(3) ∴1/x^3 = 1/2 + √(3) = 1 × (2 √(3))/(2 + √(3))(2 √(3)) =2 √(3)/(2)^2 (√(3))^2=2 √(3)/4 3 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Rationalisation

If x = √2 + √...

Question

If $x = \sqrt[3]{2 + \sqrt{3}}, t h e n x^{3} + \frac{1}{x^{3}} =$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
4

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

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

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

(Rationalising the denominator)

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

$∴ x^{3} + \frac{1}{x^{3}} = 2 + \sqrt{3} + 2 - \sqrt{3} = 4$

Suggest Corrections

Similar questions

Q. If

x = \sqrt{3} + \sqrt{2}

, then the value of

x^{3} - \frac{1}{x^{3}}

is equal to

If $x = 2 + \sqrt{3}$ , then $x^{3} + \frac{1}{x^{3}}$ = __.

Q. If

x + \frac{1}{x} = 3

, then

x^{3} + \frac{1}{x^{3}}

= _____.

Q. If

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

, then the value of

(x^{3} + \frac{1}{x^{3}})

Q. If

x = 3 + 2 \sqrt{2}

, then find the value of

x^{3} - \frac{1}{x^{3}}

Join BYJU'S Learning Program

If x=3√2+√3, then x3+1x3=

The correct option is B 4 x=(2+√3)13⇒x3=2+√3 ∴1x3=12+√3=1×(2−√3)(2+√3)(2−√3) =2−√3(2)2−(√3)2=2−√34−3 (Rationalising the denominator) =2−√31=2−√3 ∴ x3+1x3=2+√3+2−√3=4

If $x = \sqrt[3]{2 + \sqrt{3}}, t h e n x^{3} + \frac{1}{x^{3}} =$