Question

if x is positive real number and x(power)2=2,then the value of x(power)3 is

Answer 1

x² = 2

x² - 2 = 0

x² - ( √2)² = 0

use formula , a² - b² = ( a - b)(a + b)

x² - (√2)² = ( x -√2)(x + √2) = 0

x = -√2 or +√2

but question says that x is positive real number so, x ≠ -√2

hence, x = √2

now ,

x³ = (√2)³ = √2 × √2 × √2 = 2√2

x³ = 2√2

Answer 2

Given,

x²=2

x²-2=0

x²-(√2)²=0

This is in the form of a²-b²

We know that,
a²-b²=(a-b) (a+b)

=(x-√2)(x+√2)

x-√2=0 ; x=√2

x+√2=0 ; x=-√2

But according to the question,x is positive real number.

So,x≠-√2 and x=√2

x³=(√2)³

x³=√2×√2×√2

x³=2×√2

x³=2√2

Hope it helps