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Question

Solve (x5)(x7)(x+6)(x+4)=504.

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Solution

(x5)(x7)(x+6)(x+4)=504{(x5)(x+4)}{(x7)(x+6)}=504(x2x20)(x2x42)=504
Put x2x=t
(t20)(t42)=504t262t+840=504t262t+336=0t26t56t+336=0t(t6)56(t6)=0(t56)(t6)=0t=56,6x2x=t
For t=56
x2x=56x2x56=0x28x+7x56=0x(x8)+7(x8)=0(x+7)(x8)=0x=7,8
For t=6
x2x=6x2x6=0x23x+2x6=0x(x3)+2(x3)=0(x+2)(x3)=0x=2,3
so the values of x are 7,8,3 and 2

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