Question
If two numbers add up to 12 and the sum of their cubes
is 1728, then what is the product of the two numbers?Solution
ATQ,
Let the two numbers be 'a' and 'b'. a + b = 12 a³ + b³ = 1728 We know that, (a + b)³ = a³ + b³ + 3ab × (a + b) Or, (12)³ = 1728 + 3ab × 12 Or, 1728 = 1728 + 36ab Or, 1728 = 1728 + 36ab So, 36ab = 0 ⇒ ab = 0 Hence, Product of the numbers = 0
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