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Question

The largest root of the equation (x5)(x7)(x+6)(x+4)=504 is

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Solution

(x5)(x7)(x+6)(x+4)=504(x5)(x+4)(x7)(x+6)=504(x2x20)(x2x42)=504
Assuming y=x2x20, we get
y(y22)=504y222y504=0(y11)2121504=0(y11)2=625y=11±25y=14,36x2x20=14,36
So, we get two quadratic equation,
x2x6=0 and x2x56=0
Solving them,
x2x6=0(x3)(x+2)=0x=2,3x2x56=0(x8)(x+7)=0x=7,8

Hence, the largest root is 8.

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