If x2 + 1/4×2 = 8, find x3 + 1/8×3.

If x² + 1/4x² = 8, find x³ + 1/8x³.

Answer :

We know that

(x + 1/2x)² = x² + (1/2x)² + 2x (1/2x)

It can be written as

(x + 1/2x)² = x² + 1/4x² + 1

Substituting the values

(x + 1/2x)² = 8 + 1 = 9

So we get

x + 1/2x = ± √9 = ± 3

Here

x³ + 1/8x³ = x³ + (1/2x)³

We know that

x³ + 1/8x³ = (x + 1/2x)³ – 3x (1/2x) (x + 1/2x)

Substituting the values

x³ + 1/8x³ = (± 3)³ – 3/2 (± 3)

By further calculation

x³ + 1/8x³ = ± (27 – 9/2)

Taking LCM

x³ + 1/8x³ = ± (54 – 9)/ 2

x³ + 1/8x³ = ± 45/2 = ± 22 ½

Therefore, x³ + 1/8x³ = ± 22 ½.

More Solutions:

• If (x + 1/x)2 = 3, find x3 + 1/x3.
• If x = 5 – 2√6, find the value of √x + 1/√x.
• If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2.
• If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.
• If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.
• If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.
• Find the value of ab – bc – ca.
• If a – b = 7 and a2 + b2 = 85, then find the value of a3 – b3.
• Find the product of x and y.
• Find the sum of their cubes.