Question

The difference between two positive is 2 and the difference between their cubes is 56.find the number

Answer 1

Answer:4,2

Step-by-step explanation:

Let m and n be the required numbers

m-n= 2, or n= m-2 , Eq 1

m^3-n^3=56 , Eq 2

Using the formula m^3-n^3= (m-n)(m^2+mn+n^2)

56=2(m^2+ mn + n^2) , substituting values from Eq 1 and Eq 2

m^2+mn+ n^2= 28

(m-n)^2+3mn=28

4+3mn=28 , using Eq 1

3mn=24

mn=8

m(m-2)=8 , substituting for n from Eq 1

m^2–2m-8=0

m=[2+-sqrt(4+32)]/2=[ 2+-6]/2=4 or -2

Keeping only positive roots, m =4 and n=2 are the required numbers

Answer 2

Answer:

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