a-b-N-a-b-2-a-b-128-ab-

Question Number 151371 by mathdanisur last updated on 20/Aug/21

a; b \in N

{(a + b)}^{2} \cdot (a - b) = 128

ab = ?

Answered by nimnim last updated on 20/Aug/21

a; b \in N

\Rightarrow (a + b) > (a - b) \dots . (i)

we have {(a + b)}^{2} \cdot (a - b) = 128

= \underline{1^{2} \cdot 128}, \underline{2^{2} \cdot 32,} \underline{4^{2} \cdot 8}, \underline{8^{2} . 2}

Only {(a + b)}^{2} \cdot (a - b) = 8^{2} \cdot 2 satisfy (i)

\Rightarrow a + b = 8 and a - b = 2

\Rightarrow a = 5, b = 3

∴ ab = 5 \cdot 3 = 15 ★

Facebook Tweet Pin