Question

Difference between two positive integers is 2 if diffence between their cube is 56 then find the two numbers

Answer 1

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Let the one of the number be x

So, the other number is (x+2)

A/Q

$= > {(x + 2)}^{3} - {x}^{3} = 56 \\ = > {x}^{3} + 3. {x}^{2}.2 + 3.x. {2}^{2} + {2}^{3} - {x}^{3} = 56 \\ = > {x}^{3} + 6 {x}^{2} + 12x + 8 - {x}^{3} = 56 \\ = > 6 {x}^{2} + 12x - 48 = 0 \\ = > {x}^{2} + 2x - 8 = 0 \\ = > {x}^{2} + 4x - 2x - 8 = 0 \\ = > x(x + 4) - 2(x + 4) = 0 \\ = > (x + 4)(x - 2) = 0$

Either

(x+4) = 0 or (x–2) = 0

=> x = –4 (N.P) => x = 2

Therefore,

The two nos. are x = 2 and (x+2) =2+2=4

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