Question

Please help me with these answers. I am unable to do it ​

Answer 1

EXPLANATION.

Question = 6.

⇒ (x + 1/x) = 3.

As we know that,

Cube both sides of the equation, we get.

⇒ (x + 1/x)³ = (3)³.

⇒ (x³ + 3(x²)(1/x) + 3(x)(1/x²) + 1/x³) = 27.

⇒ (x³ + 3x + 3/x + 1/x³) = 27.

⇒ (x³ + 3(x + 1/x) + 1/x³) = 27.

Put the value of x + 1/x = 3 in equation, we get.

⇒ (x³ + 3(3) + 1/x³) = 27.

⇒ (x³ + 1/x³ + 9) = 27.

⇒ (x³ + 1/x³) = 27 - 9.

⇒ (x³ + 1/x³) = 18.

Question = 7.

⇒ (x - 1/x) = 5.

As we know that,

cube both sides of the equation, we get.

⇒ (x - 1/x)³ = (5)³.

⇒ (x³ - 3(x²)(1/x) + 3(x)(1/x²) - 1/x³) = 125.

⇒ (x³ - 3x + 3/x - 1/x³) = 125.

⇒ (x³ - 3(x - 1/x) - 1/x³) = 125.

Put the value of x - 1/x = 5 in equation, we get.

⇒ (x³ - 3(5) - 1/x³) = 125.

⇒ (x³ - 15 - 1/x³) = 125.

⇒ (x³ - 1/x³) = 125 + 15.

⇒ (x³ - 1/x³) = 140.

Question = 8.

⇒ (x - 2/x) = 6.

As we know that,

Cube both sides of the equation, we get.

⇒ (x - 2/x)³ = (6)³.

⇒ (x³ - 3(x²)(2/x) + 3(x)(2/x)² - (2/x)³) = 216.

⇒ (x³ - 6x + 3(x)(4/x²) - 8/x³) = 216.

⇒ (x³ - 6x + 12/x - 8/x³) = 216.

⇒ (x³ - 6(x - 2/x) - 8/x³) = 216.

Put the value of x - 2/x = 6 in equation, we get.

⇒ (x³ - 6(6) - 8/x³) = 216.

⇒ (x³ - 36 - 8/x³) = 216.

⇒ (x³ - 8/x³) = 216 + 36.

⇒ (x³ - 8/x³) = 252.

Answer 2

Solution :-

Question6 ⇒ (x + 1/x) = 3.

According to the question :-

• → (x + 1/ x)³ = (3)³.
• → (x³ + 3(x²)(1/ x) + 3(x)(1/ x²) + 1/x³) = 27.
• → (x³ + 3x + 3 /x + 1/ x³) = 27.
• → (x³ + 3(x + 1/ x) + 1 /x³) = 27.

Put the value of x + 1/x = 3 in equation.

We get,

• → (x³ + 3(3) + 1/x³) = 27.
• → (x³ + 1/x³ + 9) = 27.
• → (x³ + 1/x³) = 27 - 9.
• → (x³ + 1/x³) = 18. Ans.