Number of non-negative integral solution of eq n y 4 +6xy 2 -8x=0 is

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pranshu aggarwal Grade:


                        Number of non-negative integral solution of eq n y 4 +6xy 2 -8x=0 is equal to a) 1 b) 2 c) 3 d) infinite

9 years ago

Answers : (2)

SAGAR SINGH - IIT DELHI

879 Points

Dear student,

The correct option is b)

9 years ago

Disapproved

jagdish singh singh

173 Points

$$Here $x,y\geq0$ and $x,y\in Z$.\\\\ Now $y^4+6xy^2=8x\Leftrightarrow y^4=8x-6xy^2\Leftrightarrow y^4=2x.(4-3y^2)$\\\\ Here $y^4\geq 0$. So $2x.(4-3y^2)\geq 0$\\\\ Means either $x\geq 0$ OR $4-3y^2\geq 0\Leftrightarrow 3y^2-4\leq 0\Leftrightarrow y^2\leq \frac{4}{3}$\\\\ Means $y<2$. So Here are only Two values of $y$ i.e $y=0$ and $y=1$\\\\ If $y=0$,Then $x=0$. So one ordered pair is $\boxed{\boxed{x,y=(0,0)}}$ and\\\\ If $y=1$,Then $1+6x=8x\Leftrightarrow x=\frac{1}{2}$\\\\ So only ordered pair is $(x,y)=(0,0)$\\\\$

9 years ago

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Number of non-negative integral solution of eq n y 4 +6xy 2 -8x=0 is equal to a) 1 b) 2 c) 3 d) infinite

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