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Algebra Level 2

Given

x + x = m x+x=m ; and

x . x = m x.x=m

Where x x and m m are whole numbers. How many such x x exist so that the above conditions are satisfied.

3 2 4 1

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2 solutions

Kenny O.
Oct 8, 2017

From the equations, x 2 = 2 x x^2=2x .
Moving the 2x to the other side, we get x 2 2 x = 0 x^2-2x=0 .
Factoring, we get x ( x 2 ) = 0 x(x-2)=0 . This tells us x is either 0 or 2 (or both). When x=0, m=0. When x=2, m=4.
Thus, the answer is 2.

Ayush Kumar
Oct 7, 2017

Interestingly enough, the pairs are x = 2 , m = 4 x=2, m=4 and x = 0 , m = 0 x=0, m=0 . This is because x + x x+x is the same as 2 x 2x and x x x*x is the same as x 2 x^2 . These graphs intersect at the given points and no others. m m represents the y-coordinate of the intersections and x x obviously represents the x-coordinate.

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