The discussion revolves around solving a complex equation involving polynomial expressions of various degrees. The equation presented involves terms raised to the fourth power and is set equal to a fraction involving constants and variables.
Participants are actively engaging with the problem, asking for clarification on the reasoning behind proposed solutions and expressing confusion about the steps involved. Some guidance has been offered regarding the expansion of terms, but there is no clear consensus on the solutions or methods to proceed.
There are indications of confusion regarding the number of solutions and the nature of the polynomial equation, as well as a mention of personal circumstances affecting participation in the discussion.
evagelos said:Homework Statement
The equation is:[tex]\frac{(a-x)^4+(x-b)^4}{(a+b-2x)^2}=\frac{a^4+b^4}{(a+b)^2}[/tex]
Homework Equations
The Attempt at a Solution
I expanded the terms on the L.H.S and ended up with an equation of 4th,3rd,2nd ,1st degree equation very difficult to solve.
Susanne217 said:Am I correct to assume that you are suppose to find a solution with respect to x?
I get that x is either [tex]x = \frac{2ab}{a+b}[/tex] or [tex]\frac{a^2+b^2}{a+b}[/tex] or x = 0
evagelos said:Yes you right ,but how did you get those solutions?
But is it not there a forth solution ,or one of them is double??
Susanne217 said:1) Use the fact that (x-a)^4 = ((x-a)^2)^2 and then solve with respect to x
evagelos said:I am sorry can you elaborate a little more ,i cannot follow.