Question

If the difference of two numbers is 10 and their product is -24, find sum of their cubes.​

Answer 1

Answer:

33+53=27+125=152

Step-by-step explanation:

If the sum and product of two numbers are 8 and 15 respectively, what is the sum of their cubes?

Let our two numbers be a and b . Then we can see that a+b=8 and ab=15 . Now consider

(a+b)3=a3+3a2b+3ab2+b3 by the binomial expansion. Now we have all the information to solve this, observe since a+b=8 and ab=15 . We have

(8)3=a3+3ab(a)+3ab(b)+b3

a3+b3+3ab(a)+3ab(b)=83

a3+b3+3ab(a+b)=83

a3+b3=83−3ab(a+b)

a3+b3=83−3(15)(8)=512−360=152

You can also observe that 3 and 5 fulfill those conditions so, then 33+53=27+125=152 . Which is our result.