Question

If x,y are integral sol of $2x^2-3xy-2y^2=7$ then find $\left|x+y\right|=0$

• A. 2
• B. 4
• C. 6
• D. $2\left|4\right|6$

Answer 1

Answer: (B)

4

Given $2x^2-3xy-2y^2=7$ ; we have to find $|x+y|$ where $x$ and $y$ are the integral solution of the given equation.

Now ${2x}^2-3xy-2y^2=7$

$\Rightarrow 2x^2-4xy+xy-2y^2=7\Rightarrow 2x(x-2y)+y(x-2y)=7$

$\Rightarrow (2x+y)(x-2y)=7\times 1$ ($\therefore 7$ is a prime number it cannot be decomposed into factors.)

$\therefore$ we have two cases

$\left(i\right)2x+y=7x-2y=1$

Solving for $x$ & $y$ we get

$x=3y=1\therefore |x+y|=4$

$\left(ii\right)2x-y=1x-2y=7$

Solving for $x$ & $y$

$x=\frac{9}{5}y=\frac{-13}{5}\therefore |x+y|=\left|\frac{-4}{5}\right|=\frac{4}{5}$

But $x$ and $y$ here only represent integral solutions of the equation

$\therefore |x+y|=|3+1|=4$