Find-all-ordered-pairs-of-real-numbers-x-y-for-which-1-x-4-1-x-2-1-x-1-y-7-1-y-4-1-y-2-1-y-1-x-7-

Question Number 153012 by bobhans last updated on 04/Sep/21

F i n d a l l o r d e r e d p a i r s o f r e a l

n u m b e r s (x, y) f o r w h i c h

{\begin{cases} (1 + x^{4}) (1 + x^{2}) (1 + x) = 1 + y^{7} \\ (1 + y^{4}) (1 + y^{2}) (1 + y) = 1 + x^{7} \end{cases}

Commented by mr W last updated on 04/Sep/21

f (x) = f^{- 1} (x)

\Rightarrow y = x

(1 + x^{4}) (1 + x^{2}) (1 + x) = 1 + x^{7}

x (1 + x + x^{2} + x^{3} + x^{4} + x^{5}) = 0

\frac{x (1 - x^{6})}{1 - x} = 0

\Rightarrow x = 0, - 1

\Rightarrow s o l u t i o n i s (0, 0) o r (- 1, - 1)

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