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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

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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`

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APPEARS IN

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