Question

Solve for real $y$ and $x$

$(1+i)y^2+6+i=(2+i)x.$

• A. $x=5,y=2$ or $x=5,y=-2.$
• B. $x=-5,y=2$ or $x=5,y=2.$
• C. $x=-5,y=2$ or $x=-5,y=-2.$
• D. $x=-5,y=-2$ or $x=5,y=-2.$

Answer 1

The correct option is A $x=5,y=2$ or $x=5,y=-2.$

Simplifying, and by segregating the real and imaginary part we get
$\Rightarrow y^2-2x+6=0$ -------i()
and
$\Rightarrow y^2-x+1=0$ --------(ii)
Subtracting i from ii we get
$\Rightarrow x-5=0$
$\Rightarrow x=5$
Substituting ii, we get
$\Rightarrow y^2-4=0$
$\Rightarrow y=\pm 2$