Advertisements
Advertisements
प्रश्न
If x = \[\sqrt[3]{2 + \sqrt{3}}\] , then \[x^3 + \frac{1}{x^3} =\]
विकल्प
2
4
8
9
Advertisements
उत्तर
Given that . `x = 3sqrt(2+sqrt3)` It can be simplified as
` x^3 = 2+sqrt3`
`1/ x^3 = 1 /(2+sqrt3)`
We know that rationalization factor for `2+sqrt3` is `2- sqrt3`. We will multiply numerator and denominator of the given expression `1/(2+sqrt3)`by `2-sqrt3`, to get
`1/x^3 = 1/(2+sqrt3 ) xx (2-sqrt3)/(2-sqrt3)`
`= (2-sqrt3)/((2)^2 - (sqrt3)^2)`
`= (2-sqrt3)/(4-3)`
`=2-sqrt3`
Therefore,
`x^3 + 1/x^3 = 2 +sqrt3 +2 - sqrt3`
`= 2+2`
`=4`
APPEARS IN
संबंधित प्रश्न
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt(x^-3))^5`
If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`
Simplify:
`(x^(a+b)/x^c)^(a-b)(x^(b+c)/x^a)^(b-c)(x^(c+a)/x^b)^(c-a)`
If (x − 1)3 = 8, What is the value of (x + 1)2 ?
The value of \[\left\{ 2 - 3 (2 - 3 )^3 \right\}^3\] is
If x is a positive real number and x2 = 2, then x3 =
If \[\frac{x}{x^{1 . 5}} = 8 x^{- 1}\] and x > 0, then x =
The simplest rationalising factor of \[\sqrt[3]{500}\] is
If \[x = 7 + 4\sqrt{3}\] and xy =1, then \[\frac{1}{x^2} + \frac{1}{y^2} =\]
The value of \[\sqrt{3 - 2\sqrt{2}}\] is
