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Question

The number of different possible values for the sum x+y+z, where x,y,z are real numbers such that x4+4y4+16z4+64=32xyz is

A
1
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B
2
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C
4
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D
8
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Solution

The correct option is C 4
S=x+y+z=?x4+4y4+16z4+64=32xyzx4+4y4+16z4+644(x44y416z464)1432xyz48xyz8xyz8xyzAM=GMx4=4y4=16z4=64x=±22y=±2z=±2
But 32xyz is positive. Hence, number of possible sums are 4.

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