# If X=2^(1/3)+2^(2/3), Show that X3 - 6x = 6 - Mathematics

If x=2^(1/3)+2^(2/3), Show that x3 - 6x = 6

#### 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

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Exercise 2.2 | Q 11 | Page 26