Question
If, ( a + b = 14 ) and ( a² + b² = 106 ), then find the value of (a³ + b³).
Solution
( a + b = 14 )
( (a + b) ² = 14² )
( a² + b² + 2ab = 196 )
( 106 + 2ab = 196 )
( 2ab = 90 ab = 45 )
(a³ + b³ = (a + b)(a² + b² - ab)) = 14 (106 – 45) = 14 * 61 = 854
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