Question

if x= 2^2/3+2^1/3, then prove that x^3-6x-6=0​

Answer 1

Answer:

Taking x= 2^(2/3) + 2^(1/3) we get

x = (cube root of 2)^2 + (cube root of 2)

[ Because power 1/3 is nothing but cube root]

Let's first find x^3,

x^3 = [ (cube root of 2)^2 + (cube root of 2) ]^3

Using (a+b)^3 formula we get

x^3 = 6 + 6[ 2^(2/3) + 2^(1/3) ]

Now let's find out 6x,

6x = 6( 2^(2/3) + 2^(1/3) )

Taking the equation x^3 - 6x -6 as A,

A = 6 + 6[ 2^(2/3) + 2^(1/3) ] - 6( 2^(2/3) + 2^(1/3) ) -6

Which gives A = 0.

Therefore x^3 - 6x - 6 = 0.

Hence proved.

Step-by-step explanation:

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