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If a-b = 2 and ab = 15 then find out a3-b3 |
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Answer» HELLO !! a - B = 2 ---------(1) and, a b = 15 -------(2) From equation (1) we get, a - b = 2 a = ( 2 + b ) ------(3) Putting the value of a in equation (2) a × b = 15 (2 + b ) × b = 15 b² + 2b - 15 = 0 b² + 5b - 3b - 15 = 0 b ( b + 5 ) - 3 ( b + 5 ) = 0 ( b + 5 ) ( b - 3 ) = 0 ( b -3 ) = 0 or ( b + 5 ) = 0 b = 3 or b = -15 Putting B = 3 in equation (3) a = ( 2 + b ) = (2+3) = 5 ---------------------------- ( A³ - B³ ) = ( A - B )( A² + AB + B²) ( A³ - B³ ) = ( 2 ) [ ( 5)² + 15 + (2)² ] ( A³ - B³ ) = ( 2 ) × ( 44 ) ( A³ - B³ ) = 88 |
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