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Question

The number of positive integral solutions of the equation dety3+1y2zy2xyz2z3+1z2yx2xzx3+1=11 is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is C 3
Multiply by y,z and x in rows 1,2 and 3 respectively and then take common y, z and x from column 1,2 and 3 respectively, then
dety3+1y3y3z3z3+1z3x3x3x3+1=11
det10y311z301x3+1=11(C1C1C2 and C2C2C3)(x3+1+z3)+y3(1)=11x3+y3+z3=10So solution are (1,1,2),(1,2,1) or (2,1,1)

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