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 a = 3 and b = -2, find the values of :
ab + ba
If abc = 1, show that `1/(1+a+b^-1)+1/(1+b+c^-1)+1/(1+c+a^-1)=1`
Simplify the following:
`(5xx25^(n+1)-25xx5^(2n))/(5xx5^(2n+3)-25^(n+1))`
Prove that:
`sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
Find the value of x in the following:
`2^(5x)div2x=root5(2^20)`
Find the value of x in the following:
`5^(2x+3)=1`
Solve the following equation:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Write \[\left( 625 \right)^{- 1/4}\] in decimal form.
If \[2^{- m} \times \frac{1}{2^m} = \frac{1}{4},\] then \[\frac{1}{14}\left\{ ( 4^m )^{1/2} + \left( \frac{1}{5^m} \right)^{- 1} \right\}\] is equal to
If `a = 2 + sqrt(3)`, then find the value of `a - 1/a`.
