Question

Ravita donated Rs (x^3+ 1/x^3) to blind school. Her friends wanted to know the amount donated by her. She did not disclose the amount but gave a hint that x + 1/x = Rs 8, the amount donated by Ravita to blind school is​

Answer 1

Given,

Amount donated by Ravita = x³ + 1/x³

Hint given by Ravita = x + 1/x = Rs 8

To find,

The amount donated by Ravita to the blind school

Solution,

Ravita has given a hint to her friends about the money donated,

x + 1/x = Rs 8

Cubing both the sides

(x + 1/x)³ = 8³

(x + 1/x)³ = 512

x³ + 1/x³ + (3 × x × 1/x) (x + 1/x)

x³ + 1/x³ + 3 (x + 1/x) = 512    

We know that the value of x +1/x  is 8.

∵ x³ + 1/x³ + 3 × 8 = 512

x³ + 1/x³ + 3 × 8 = 512

x³ + 1/x³ + 24 = 512

x³ + 1/x³ = Rs 488

Therefore, the amount donated by Ravita to the blind school is Rs 488.