Question

X*x+y*y-10=0 Write the values of y, for which the equation have sense.

Answer 1

Answer:

The equation is defined for y values in the closed interval $[-\sqrt{10},\sqrt{10}]$.

Step-by-step explanation:

$x^2+y^2-10=0\\\implies x^2 = 10-y^2$

Since x^2 is a non-negative quantity, this implies the following inequality must hold:

$10-y^2\geq0\\y^2\leq 10\\|y|\leq \sqrt{10}\\\implies -\sqrt{10}\leq y \leq \sqrt{10}$

In other words, y must lie between $\pm \sqrt{10}$, inclusively.