Question

Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 10, the sum of the squares of the numbers is 29, and the sum of the cubes of the numbers is 133.

Enter your answer as a number, like this: 42

Answer 1

x+y = 7

Explanation:

We have given that

The product of the numbers is 10

xy = 10

The sum of the squares of the numbers is 29

x²+y² = 29

The sum of the cubes of the numbers is 133

x³+y³ = 133

We have to find that the sum of two numbers.

x+y = ?

Using given formula, we have

(x+y)(x²-xy+y²) = x³+y³

(x+y)(x²+y²-xy) = x³+y³

Putting given value in above formula, we have

(x+y)(29-10) = 133

(x+y)(19) = 133

(x+y) = 133 / 19

x+y = 7 which is the answer.

Answer 2

The sum of two numbers is 7.

Explanation:

Given : the product of the numbers is 10, the sum of the squares of the numbers is 29, and the sum of the cubes of the numbers is 133.

Using identity
`(x+y)(x^2-xy+y^2)=x^3+y^3` and given details, we have to find the sum of two numbers.

Since, given that the product of the numbers is 10 that is
`xy=10`

Also, given the sum of the squares of the numbers is 29 that is
`x^2+y^2=29`

and the sum of the cubes of the numbers is 133 that is
`x^3+y^3=133`

Using, the given identity
`(x+y)(x^2-xy+y^2)=x^3+y^3`,

Substitute, the given values, we have,

`(x+y)(29-10)=133`

Simplify , we get,

`(x+y)(19)=133`

Divide both side by 19, we have,

`(x+y)=7`

Thus, the sum of two numbers is 7.