Determine all pairs of real numbers (a;b) such that: a^6 −b^4 =b^6 −a^4 =4


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
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

$c o o l S e r t h a n k s, y = \pm \sqrt{2} \Rightarrow b = \pm \sqrt{2} . ?$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum