Question

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

Answer 1

Let the two numbers be x and y
Sum of numbers = 8
x+y = 8
x = 8-y

Product of numbers = 15
xy = 15
y(8-y) = 15
8y - y² = 15
y² - 8y + 15 =0
y² - 5y -3y +15 =0
y(y-5) -3(y-5) = 0
(y-5)(y-3) = 0
y = 5 or y = 3

If y = 5 then x = 3
If y = 3 then x = 5
the two numbers are 3 and 5

Their cubes are 27 and 125

Answer 2

Step-by-step explanation:

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

-(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