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Question

The number of real integral solution(s) of the equation, (x+9)(x3)(x7)(x+5)=385 is(are)
  1. 2

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Solution

The correct option is A 2
The given equation is (x+9)(x3)(x7)(x+5)=385.
This is a type 2 biquadratic equation.
On rearranging the terms and opening the bracket, we get,
(x+9)(x7)(x3)(x+5)=385
(x+9)(x7)(x+5)(x3)=385
(x2+2x63)(x2+2x15)=385
Put x2+2x=z
(z63)(z15)=385
z278z+945=385
z278z+560=0
z270z8z+560=0
(z70)(z8)=0
z=70 or 8

x2+2x=70
x2+2x70=0
x=2±4+2802
x=2±2842
x=1+71$or$171

x2+2x=8
x2+2x8=0
x=2±4+322
x=2 or 4

x=2,4,1+71,171
Hence, the number of real integral solutions is2 i.e x=2,4

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