Determine-all-pairs-of-real-numbers-a-b-such-that-a-6-b-4-b-6-a-4-4-

Question Number 146377 by mathdanisur last updated on 13/Jul/21

D e t e r m i n e a l l p a i r s o f r e a l n u m b e r s

(a; b) s u c h t h a t :

a^{6} - b^{4} = b^{6} - a^{4} = 4

Commented by mr W last updated on 13/Jul/21

a = b = \pm \sqrt{2}

Commented by mathdanisur last updated on 13/Jul/21

t h a n k y o u S e r, s o l u t i o n

Commented by mr W last updated on 13/Jul/21

x = a^{2}

y = b^{2}

x^{3} - y^{2} = y^{3} - x^{2} = 4

x^{3} + x^{2} = y^{3} + y^{2}

\Rightarrow x = y

x^{3} - x^{2} = 4

x^{2} (x - 1) = 4

\Rightarrow x = 2 \Rightarrow a = \pm \sqrt{2}

\Rightarrow y = 2 \Rightarrow b = \pm \sqrt{2}

Commented by mathdanisur last updated on 13/Jul/21

c o o l S e r t h a n k s, y = \pm \sqrt{2} \Rightarrow b = \pm \sqrt{2} . ?