x3 + y3 = (x+y)(x2 + y2 -xy) =x2 + y2 -xy = (x+y)2 -3xy = 1-3xy=a
x5 + y5 = (x+ y)(x4 -x3.y + x2y2 - xy3 + y4) = (x4 + y4 + x2y2) - (x3.y + xy3) = (x2 + y2)2 - x2y2 - xy (x2 + y2)
= [(x+y)2 - 2xy]2 - x2y2 -xy [(x+y)2 -2xy] = (1-2xy)2 - x2y2 -xy(1-2xy) = 4x2y2 -4xy +1 - x2y2 - xy+ 2x2y2
= 5x2y2 -5xy +1 = b
xét 5a(a+1) = 5(1-3xy)(1-3xy+1) = 5(1-3xy)(2-3xy) = 5 (2-9xy+ 9x2y2) = 10 - 45xy + 5x2y2 = 9( 5x2y2 -5xy +1 ) + 1 = 9b + 1
=> đpcm
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