Question

If x+1/x = root 7 then find x^3 + 1/x^3

Answer 1

Step-by-step explanation:

Given -

◕ x + 1/x = √7

To Find -

➳ Value of x³ + 1/x³

Now,

⇝x + 1/x = √7

Cubing both sides :-

⇝ (x + 1/x)³ = (√7)³

⇝ x³ + 1/x³ + 3x²/x + 3x/x² = 7√7

⇝ x³ + 1/x³ + 3x + 3/x = 7√7

⇝ x³ + 1/x³ + 3(x + 1/x) = 7√7

⇝ x³ + 1/x³ = 7√7 - 3(x + 1/x)

⇝ x³ + 1/x³ = 7√7 - 3(√7)

⇝ x³ + 1/x³ = 7√7 - 3√7

⇝ x³ + 1/x³ = 4√7

Hence,

The value of x³ + 1/x³ is 4√7.

Answer 2

Hey GUYS. .

Hope you like this ANSWER.

Step-by-step..

Given -

◕ x + 1/x = √7

To Find -

➳ Value of x³ + 1/x³

Now,

⇝x + 1/x = √7

Cubing both sides :-

⇝ (x + 1/x)³ = (√7)³

⇝ x³ + 1/x³ + 3x²/x + 3x/x² = 7√7

⇝ x³ + 1/x³ + 3x + 3/x = 7√7

⇝ x³ + 1/x³ + 3(x + 1/x) = 7√7

⇝ x³ + 1/x³ = 7√7 - 3(x + 1/x)

⇝ x³ + 1/x³ = 7√7 - 3(√7)

⇝ x³ + 1/x³ = 7√7 - 3√7

⇝ x³ + 1/x³ = 4√7

Hence,

The value of x³ + 1/x³ is 4√7....

Thanks for this question.