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Advocard [28]
3 years ago
10

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

Mathematics
1 answer:
rodikova [14]3 years ago
4 0

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.

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