If a-b = 2 and ab = 15 then find out a3-b3
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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
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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