Question

if the sum and the product of 2 numbers are 8 and 15 find the sum of their cubes​

Answer 1

Answer:

x + y = 8

y = 8 - x

xy = 15

y = 15/x

8 - x = 15/x

x (8 - x) = 15

-x^2 + 8x = 15

-x^2 + 8x - 15 = 0

- (x^2 - 8x + 15) = 0

- (x - 3) (x - 5) = 0

x-3 = 0; x = 3

x - 5 = 0; x = 5

x + y = 8

3 + y = 8

y = 5

5 + y = 8

y = 3

x^3 + y^3

3^3 + 5^3

27 + 125

152

The x,y combination is either x = 3 and y = 5 or x = 5 and y = 3; regardless of the combination, the sum of their cubes is 154

Answer 2

Answer:

152

Step-by-step explanation:

Let the numbers are 'a' and 'b'.

Given, sum = a + b = 8 ...(1)

product = ab = 15 ... (2)

Cube on both sides of (1):

=> (a + b)³ = 8³

=> a³ + b³ + 3ab(a + b) = 512

=> a³ + b³ + 3(15)(8) = 512 ...{from(2)&(1)}

=> a³ + b³ + 360 = 512

=> a³ + b³ = 152

=> (cube of a) + (cube of b) = 152

=> sum of cubes of a & b = 152

Aa desired, sum of their cubes is 152