Find all pairs of real numbers (a,b) such that (x-a)^2+(2x-b)^2=(x-3)+(2x^2)

Question

Give an explanation on how to solve it please.

Answer 1

I assume this means that the constants a and b are supposed to make the equation true for all x. You do this by multiplying out the binomials and equating the terms containing like powers. (quadratic, linear, constant)

In this case, you are out of luck because the quadratic term leads to

x²+4x² = 2x² which cannot be made true for all x.

I assume that there is something wrong with the way the equation is written:

Here are the linear and constant term grouping results:

-2ax -4bx = x or -2a-4b = 1

a² + b² = -3 (no real solution)

Sorry, that must not have been the problem. If it is and it's just a matter of fixing the statement, than you can use this procedure to solve for a and b.