Question
If, ( a + b = 20 ) and ( a² + b² = 208 ), then find
the value of (a³ + b³).Solution
( a + b = 20 )
( (a + b)² = 20² )
( a² + b² + 2ab = 400 )
( 208 + 2ab = 400 )
( 2ab = 192 ab = 96 )
(a³ + b³ = (a + b)(a² + b² - ab)) = 20 (208 - 96) = 20 * 112 = 2240)
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