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Maths-

General

Easy

Question

The number of positive integral solutions of the equation $open vertical bar table row cell y to the power of 3 end exponent plus 1 end cell cell y to the power of 2 end exponent z end cell cell y to the power of 2 end exponent x end cell row cell y z to the power of 2 end exponent end cell cell z to the power of 3 end exponent plus 1 end cell cell z to the power of 2 end exponent x end cell row cell y x to the power of 2 end exponent end cell cell X to the power of 2 end exponent Z end cell cell x to the power of 3 end exponent plus 1 end cell end table close vertical bar equals 11$ is

1
2
3
4

The correct answer is: 3

Multiply by y, z and x in rows 1,2 and 3 respectively and then take common y, z and x fr om column 1, 2 and 3 respectively, then
$open vertical bar table row cell y to the power of 3 end exponent plus 1 end cell cell y to the power of 3 end exponent end cell cell y to the power of 3 end exponent end cell row cell z to the power of 3 end exponent end cell cell z to the power of 3 end exponent plus 1 end cell cell z to the power of 3 end exponent end cell row cell x to the power of 3 end exponent end cell cell x to the power of 3 end exponent end cell cell x to the power of 3 end exponent plus 1 end cell end table close vertical bar equals 11$
$left parenthesis C subscript 1 end subscript rightwards arrow C subscript 1 end subscript minus C subscript 2 end subscript$ and $C subscript 2 end subscript rightwards arrow C subscript 2 end subscript minus C subscript 3 end subscript right parenthesis$
$equals 1 left parenthesis x to the power of 3 end exponent plus 1 plus z to the power of 3 end exponent right parenthesis plus y to the power of 3 end exponent left parenthesis 1 right parenthesis equals 11 equals x to the power of 3 end exponent plus y to the power of 3 end exponent plus z to the power of 3 end exponent equals 10$
So solution are $left parenthesis 1 comma blank 1 comma blank 2 right parenthesis$ , $left parenthesis 1 comma blank 2 comma blank 1 right parenthesis$ or $left parenthesis 2 comma blank 1 comma blank 1 right parenthesis$

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