SOLUTION: Find all the real numbers that satisfy the given equation x⁴ + (2

SOLUTION: Find all the real numbers that satisfy the given equation x⁴ + (2 - x)⁴ = 34

Question 1209568: Find all the real numbers that satisfy the given equation
x⁴ + (2 - x)⁴ = 34
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The expressions "x" and "2-x" are symmetric about the expression "1-x".

So define a new variable:

y = 1-x

Then...

x = 1-y
2-x = 2-(1-y) = 1+y

Now the equation is

or

The problem asks for the real number solutions, so

ANSWERS: and

Those solutions are easily verified using a graphing calculator like the TI-84.

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