Question

the difference between two positive numbers is 4 and the difference between their cubes is 316 ,find thier product

Answer 1

Answer:

58

Step-by-step explanation:

Let two positive numbers are  a  And  b  .  

As given  

a  -  b  =  4                   ------------- ( 1 )

And

a^3  - b^3  = 316                   --------- ( 2 )  

i ) Their products  

We know  

( a -  b  )^3  = a^3 b^3 -3ab  

( a -  b  )               Substitute all values from equation 1 and 2 , we get

(  4  )3 = 316 - 3ab ( 4  )

64 = 316 -   12 ab  

12ab  = 252  

ab   =   21                             ------------ ( 3 )

SO,

Their product will be   =  21                                            ( Ans  )

ii ) The sum of their squares

We know

a3 - b3   = ( a  - b ) ( a2  + ab  + b2 )  

Substitute all values from equation 1 , 2 and 3 , we get  

316  = 4 ( a2 + 21  + b2 )  

( a2 + 21  + b2 )  = 79  

a2 +  b2   =   79   -    21  

a2 +  b2  =   58  

So,

The sum of their squares   =    58                                        ( Ans )