# Thread: what is the unique values of a

1. ## what is the unique values of a

can anybody please do me a favor on this problem

Thank you so very much.

2. Equation 1 + Equation 2:

$\displaystyle \displaystyle (x^2-y^2) + [(x-a)^2+y^2] = 0+0$

$\displaystyle \displaystyle x^2 + x^2 - 2ax + a^2 = 0$

$\displaystyle \displaystyle 2x^2 - 2ax + a^2 = 0$.

This is a quadratic. For a unique solution, $\displaystyle \displaystyle \Delta = 0$.

$\displaystyle \displaystyle (-2a)^2 - 4(2)(a^2) = 0$

$\displaystyle \displaystyle 4a^2 - 8a^2 = 0$

$\displaystyle \displaystyle -4a^2 = 0$

$\displaystyle \displaystyle a = 0$.

So this system will have a unique solution when $\displaystyle \displaystyle a = 0$.

3. so amazing sir Prove it, there is one thing i would like to ask hope you wouldn't mind... how did u get the (-2a)^2 -4(2)(a) = 0 ?

thanks a lot

4. Originally Posted by rcs
so amazing sir Prove it, there is one thing i would like to ask hope you wouldn't mind... how did u get the (-2a)^2 -4(2)(a) = 0 ?

thanks a lot
For a quadratic in the form $\displaystyle ax^2+bx+c=0$ , it has one solution if $\displaystyle b^2-4ac=0$

5. ahh ic the discriminant.. thank you so so much sir pickslides