Advertisements
Advertisements
Question
If `x=2^(1/3)+2^(2/3),` Show that x3 - 6x = 6
Advertisements
Solution
x3 - 6x = 6
`x=2^(1/3)+2^(2/3)`
Putting cube on both the sides, we get,
`x^3=(2^(1/3)+2^(2/3))^3`
As we know, `(a+b)^3=a^3+b^3+3ab(a+b)`
`x^3=(2^(1/3))^3+(2^(2/3))^3+3(2^(1/3))(2^(2/3))(2^(1/3)+2^(2/3))`
`x^3=(2^(1/3))^3+(2^(2/3))^3+3(2^(1/3+2/3))(x)`
`x^3=(2^(3/3))+(2^(6/3))+3(2)(x)`
`x^3=2^1+2^2+3(2)(x)`
`x^3=2+4+6x`
`x^3=6+6x`
`x^3-6x=6`
APPEARS IN
RELATED QUESTIONS
If `27^x=9/3^x,` find x.
If `3^(x+1)=9^(x-2),` find the value of `2^(1+x)`
If `x = a^(m + n), y = a^(n + l)` and `z = a^(l + m),` prove that `x^my^nz^l = x^ny^lz^m`
State the quotient law of exponents.
Which one of the following is not equal to \[\left( \sqrt[3]{8} \right)^{- 1/2} ?\]
If g = `t^(2/3) + 4t^(-1/2)`, what is the value of g when t = 64?
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
The value of \[\sqrt{3 - 2\sqrt{2}}\] is
Find:-
`125^(1/3)`
Simplify:
`(1^3 + 2^3 + 3^3)^(1/2)`
