Irene S.

asked • 04/20/17

I have the equation (x-a)(x-b)=c^(2). I now have to prove that it has infinite solutions

I have to prove that the equation
(x-a)(x-b)=c2    has infinite solutions

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Arturo O. answered • 04/20/17

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If the variable is x, with a, b, and c being constants, then you will have a quadratic equation in x, which will have at most 2 solutions.
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Irene S.

What makes it a quadratic equation?
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04/20/17

Arturo O.

Expand (x - a)(x - b) = c2 and get
 
x2 - bx - ax + ab = c2
 
Group like terms and get
 
x2 - (b + a)x + (ab - c2) = 0
 
Note this is an equation of the form
 
Ax2 + Bx + C = 0,
 
which is a quadratic equation, with
 
where A = 1, B = -(b + a), and C = ab - c2
 
Its solution is 
 
x = [-B ± √(B2 - 4AC)] / (2A)
 
This gives at most 2 different solutions if the argument of the square root is not zero.
 
 
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04/20/17

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