Question

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

Answer 1

Let the two numbers be x and y

According to the first condition

x+y=8

x=8-y ...(i)

According to the second condition

xy=15

(8-y)y=15 .....(From i)

8y-y^2=15

y^2-8y+15=0

y^2-5y-3y+15=0

y (y-5)-3 (y-5)=0

(y-3)(y-5)=0

y=3,5

Substituting the value of y in equation (i) We get

x=8-3=5 or x=8-5=3

Now, Sum of their cubes

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 152