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Question

The roots of the equation (3x)4+(2x)4=(52x)4 are


A

2 real and 2 non real complex

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B

All are non real complex

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C

3 are real & one non real complex

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D

All real

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Solution

The correct option is A

2 real and 2 non real complex


(3x)4+(2x)4=(52x)4

Put a=3x,b=2x

a4+b4=(a+b)4

a4+b4=a4+4a3b+6a2b2+4ab3+b4

2ab(2a2+3ab+2b2)=0

a=0 or b=0 or 2a2+3ab+2b2=0

i.e., 3x=0 or 2x=0 or 7x235x+44=0

Solving we get x=3,x=2,x=(35± i 7)14


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