Number of non-negative integral solution of eqn y4+6xy2-8x=0 is equal to a) 1 b) 2 c) 3 d) infinite

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Algebra

Number of non-negative integral solution of eqⁿy⁴+6xy²-8x=0 is equal to

a) 1 b) 2

c) 3 d) infinite

pranshu aggarwal

15 Years agoGrade

2 Answers

SAGAR SINGH - IIT DELHI

15 Years ago

Dear student,

The correct option is b)

jagdish singh singh

Approved Tutor Answer15 Years ago

$$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 $(x,y)=(0,0)$\\\\$