Question

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

Answer 1

Answer:

15–8= 7

7+2 = 8

7+8= 15

ANS= 15

Answer 2

Let :

• 1st Number = x
• 2nd Number = y

Given :

• (x+y) = 8
• xy = 15

To find :

• x³ + y³

Identity used :

1. a³ + b³ = (a + b)(a² – ab + b² )
2. (a+b)² = (a²+b²+2ab)

Solution :

• using identity , (a+b)² = (a²+b²+2ab

=> (x+y)² = x²+y² + 2xy

putting respective values , we get;

=> (8)² = (x²+y²) + 2×(15)

=> 64 = (x²+y²) + 30

=> (x²+y²) = 64-30 = 34

• using identity , a³ + b³ = (a + b)(a² – ab + b² )

=> x³ + y³ = (x+y) (x² + y² - xy)

putting respective values, we get;

=> x³ + y³ = (8)×( 34 - 15)

=> x³ + y³ = (8)×(19)

=> x³ + y³ = 152

ANSWER :

Sum of cube of number = 152