Question

solve for x if possible (m2+n2)x2+(m+n)x+1/2 =0

Answer 1

Hey !!

Check the attachment.
As you can see , the above expression has complex roots.
Hope it helps you :)

Answer 2

Answer:

$x_1=\frac{-(m+n)+(m-n)i}{2(m^2+n^2)}$

$x_2=\frac{-(m+n)-(m-n)i}{2(m^2+n^2)}$         

Step-by-step explanation:

Given : Expression $(m^2+n^2)x^2+(m+n)x+\frac{1}{2}=0$

To find : Solve for x?

Solution :

Applying quadratic formula of quadratic equation $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

On comparing with given expression,

$a=(m^2+n^2), b=(m+n), c=\frac{1}{2}$

Substitute the value in the formula,

$x=\frac{-(m+n)\pm\sqrt{(m+n)^2-4(m^2+n^2)(\frac{1}{2})}}{2(m^2+n^2)}$

$x=\frac{-(m+n)\pm\sqrt{-(m^2+n^2-2mn)}}{2(m^2+n^2)}$

$x=\frac{-(m+n)\pm\sqrt{-(m-n)^2)}}{2(m^2+n^2)}$

$x=\frac{-(m+n)\pm(m-n)i}{2(m^2+n^2)}$

The solution for x are

$x_1=\frac{-(m+n)+(m-n)i}{2(m^2+n^2)}$

$x_2=\frac{-(m+n)-(m-n)i}{2(m^2+n^2)}$