If a3 335 b3 and a 5 b then what is the value of a b given that a gt 0 and b gt 0 ........

Quantitative Aptitude (CDS) Simplification

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If a³ = 335 + b³ and a = 5 + b , then what is the value of a + b (given that a > 0 and b > 0)?

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Explanation:

As, a³ = 335 + b³
=>a³ − b³= 335 ……… (i)
Also,
a = 5 + b
=>a − b = 5 ………. (ii)
Cubing both sides
a³− b³ − 3ab(a − b) = 125 ……….. (iii)
From (i) and (ii) we get,
335 − 3ab(a − b) = 125 ………. (iv)
From (ii) and (iv) we get,
335 − 3ab × 5 = 125
=> 15ab = 335 − 125
=> 15ab = 210
=> ab =210/15=14
Also, (a + b)² = (a − b)² + 4ab
=> (a − b)² = (5)²+ 4 × 14
= 25 + 56 = 81
∴ a + b = 9
Hence option (2)