Question

if x+1/x=5 find value of x3+1/x3?

Answer 1

Step-by-step explanation:

Given -

• x + 1/x = 5

To Find -

• Value of x³ + 1/x³

Now,

→ x + 1/x = 5

Cubing both sides :-

→ (x + 1/x)³ = (5)³

→ x³ + 1/x³ + 3x²/x + 3x/x² = 125

→ x³ + 1/x³ = 125 - 3x - 3/x

→ x³ + 1/x³ = 125 - 3(x + 1/x)

→ x³ + 1/x³ = 125 - 3(5)

→ x³ + 1/x³ = 125 - 15

→ x³ + 1/x³ = 110

Hence,

The value of x³ + 1/x³ is 110

Answer 2

$\large{\sf{\underline{\underline{ANSWER}}}}$

GIVEN:-

• $\huge{x+\frac{1}{x}}$

TO FIND:-

• $\huge{x^3+\frac{1}{x^3}}$

Now,

$(x+\frac{1}{x})^3=x^3+\frac{1}{x^3}×3×x×\frac{1}{x}(x+\frac{1}{x})$

Now put the values,

$(5)^3=x^3+\frac{1}{x^3}×3(5)$

$125-15=x^3+\frac{1}{x^3}$

$110=x^3+\frac{1}{x^3}$

Extra Information

• $(a+b)^2=a^2+b^2+2ab$

• $(a-b)^2=a^2-2ab+b^2$

• $a^3+b^3=(a+b)(a^2-ab+b^2)$