_Minimals_

Geometry Level 2

If A and B are nonnegative integers such that the line 8x+Ay=B contains the origin,find the minimum value of A²-B?

The answer is 0.

1 solution

John Aries Sarza
Sep 1, 2014

Take note that if ${ x }_{ int }\quad \& \quad { y }_{ int }$ are equal to $0$ then $B$ must be equal to zero. Since A and B are both non-negative integer, therefore the min value is $\boxed{1}$

The minimum value is 0, with $A=0, B=0$ .

I've updated the answer accordingly.

Calvin Lin Staff - 6 years, 9 months ago

If A can be 0, then the line wont exist? With B as 0, y = -8x / A, so A cannot be 0. The min nonnegative value of A should be 1.

prashanth adamane - 6 years, 9 months ago

The equation will be $8 x + 0 y = 0$ . This is the line $x = 0$ .

Note that you cannot divide by 0. Hence, when you divided by $A$ , you were already assuming that it is non-zero. As such, you cannot use that to conclude that A is non-zero.

Calvin Lin Staff - 6 years, 9 months ago

_Minimals_

The answer is 0.

1 solution

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