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Introduction to Algebraic Identities

The sum of tw...

Question

The sum of two numbers is 9 and their product is 20. Find the sum of their cubes.

A

189

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B

1269

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C

190

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D

79

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Solution

The correct option is A 189
Given sum of two numbers is 9 and their product is 20.

Let the numbers be a and b.

a + b = 9

ab = 20

Cubing on both sides gives
(a + b)3 = 93
a³+ b³+ 3ab(a + b) = 729
a³+ b³+ 60(9) = 729
a³+ b³= 729 - 540 = 189
a³+ b³= 729 - 540 = 189

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