Question

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

Answer 1

Step-by-step explanation:

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.

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Answer 2

Answer :

Sum of cubes of the two numbers is 152 .

Solution :

Let the two numbers be x and y .

Here ,

It is given that , the sum and the product of the two numbers are 8 and 15 respectively .

Thus ,

x + y = 8

xy = 15

Here ,

We need to find the sum of cubes of the two numbers , ie. x³ + y³ .

Now ,

We know that ;

=> (x + y)³ = x³ + y³ + 3xy(x + y)

=> 8³ = x³ + y³ + 3•15•8

=> 512 = x³ + y³ + 360

=> x³ + y³ = 512 - 360

=> x³ + y³ = 152

Hence ,

Sum of cubes of the two numbers is 152 .