Question

2 nos. are in the ratio 2:1. sum of their cubes is 1125. find the nos.​

Answer 1

Answer:

Required two numbers are 10 and 5.

Step-by-step explanation:

Let,

Required numbers are 2a and a, since they satisfy the conditions.

According to the question : Sum of cubes of both the numbers is 1125.

It means : cube of 2a + cube of a = 1125

= > ( 2a )^3 + ( a )^3 = 1125

= > 8a^3 + a^3 = 1125

= > 9a^3 = 1125

= > a^3 = 1125 / 9

= > a^3 = 125

= > a^3 = 5^3

= > a = 5

Thus,

Required numbers are :

• 2a = 2( 5 ) = 10
• a = 5

Hence the required two numbers are 10 and 5.

Answer 2

Answer:

let the numbers be 2x and x

Accordingly

(2x)³ + x³ = 1125

=) 8x³+x³ = 1125

=) 9x³ = 1125

=) x³ = 1125÷9

=) x³ = 125

=) x = 5

therefore the numbers are

5 and 10