Question

If 2x + 1/2x = 8, then find 8x^ 3 +1/8x ^3

Answer 1

Answer:

The value of 8x^3 + (1/8x^3) is 488.

Step-by-step explanation:

Given:-

2x + (1/2x) = 8

To find:-

Value of 8x^3 + (1/8x^3)

Solution:-

We have,

2x + (1/2x = 8

Cubing on both sides, we get

=> [2x + (1/2x)]^3 = (8)^3

Now, our Equation in the form of;

• (a+b)^3 = a^3 + b^3 + 3ab(a + b)

• where, a = 2x and b = (1/2x), we get

=> [(2x)^3 + (1/2x)^3 + 3(2x)(1/2x){2x + (1/2x)] = 512

=> [8x^3 + (1/8x^3) + 3{2x + (1/2x)] = 512

since: [2x + (1/2x) = 8] Given

=> [8x^3 + (1/8x^3) + 3(8)] = 512

=> [8x^3 + (1/8x^3) + 24] = 512

=> 8x^3 + (1/8x^3) = 512 - 24

=> 8x^3 + (1/8x^3) = 488

Answer:-

Hence, the value of 8x^3 + (1/8x^3) is 488.

Used formulae:-

(a+b)^3 = a^3 + b^3 + 3ab(a + b)