I bet you can't make this one

Algebra Level 5

$\begin{cases} a(x^4+1)=y+1-|x| \\ x^2+y^2=1 \end{cases}$

Find sums of all parameters $a$ such that the system of equations above have only one real solution.

The answer is 2.

1 solution

Вук Радовић
Sep 30, 2015

Let assume that $(x_0, y_0)$ is solution of our system then one may see that $(-x_0, y_0)$ is also solution of our system.

It is cleared because we want only one solution that $x_0=0$ and $y_0=-1,1$

When you now solve the equation for $a$ you will easy get $a=0,2$ . If you put back your solutions for $a$ you will see that for $a=0$ there is indeed more solution. So the final answer is $a=2$

I bet you can't make this one

The answer is 2.

1 solution

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