why is the minimum value of x^2+y^2 zero?

Answer 1

The minimum value is when x and y both equal zero.

Any other value would be greater. This is because any number, even if it is negative, squared gives a positive number. Two positive numbers produce a positive sum. Which means that the smallest number possible is 0, when both x and y are zero.


Hope this helps.

Answer 2

Get REAL, shortstac! The square of any non-zero REAL number is positive. But if both (real ) x and y are zero, you'll get zero, clearly the minimum possible for real numbers.

But if, however, you are a more COMPLEX character, then of course there is no such minimum: if x = 3i and y = 4i, the value of the given function will be -9 + (-16) = -25, i.e. less than zero!

Live long and prosper.

Answer 3

Any number, x or y, either positive or negative, when placed in your formula will give a resulting number greater than zero. (positive)
The square of any number is always positive.
The square of zero is zero.
Thus the minimum value possible is zero.

Answer 4

because even if x and y equal negative numbers, the answer will still be positive. a negative number squared equals a positive number. but 0 squared equals 0 so 0^2+0^2=0

Answer 5

squares are always positive or zero. negative numbers squared give positive results.

Answer 6

if x or y is a negative number, their products will still be positive, becuase they are squared, and a negative times a negative is a positive