Question

Find the value of a if 2x2+ay2-3x+2y-1=0

Answer 1

Answer:

$2x^2+ay^2-3x+2y-1=0\quad :\quad a=\dfrac{-2x^2+3x-2y+1}{y^2};\quad \:y\ne \:0$

Step-by-step explanation:

$2x^2+ay^2-3x+2y-1=0$

$\mathrm{Subtract\:}2x^2-3x+2y\mathrm{\:from\:both\:sides}$

$2x^2+ay^2-3x+2y-1-\left(2x^2-3x+2y\right)=0-\left(2x^2-3x+2y\right)$

$\mathrm{Simplify}$

$ay^2-1=-\left(2x^2-3x+2y\right)$

$\mathrm{Add\:}1\mathrm{\:to\:both\:sides}$

$ay^2-1+1=-\left(2x^2-3x+2y\right)+1$

$\mathrm{Simplify}$

$ay^2=-2x^2+3x-2y+1$

$\mathrm{Divide\:both\:sides\:by\:}y^2;\quad \:y\ne \:0$

$\dfrac{ay^2}{y^2}=-\dfrac{2x^2}{y^2}+\dfrac{3x}{y^2}-\dfrac{2y}{y^2}+\dfrac{1}{y^2};\quad \:y\ne \:0$

$\mathrm{Simplify}$

$a=\dfrac{-2x^2+3x-2y+1}{y^2};\quad \:y\ne \:0$