Question-69111

Question Number 69111 by Fawole last updated on 20/Sep/19

Commented by Rasheed.Sindhi last updated on 20/Sep/19

(2, 11), (11, 2), (5, 10) & (10, 5) .

Commented by Fawole last updated on 20/Sep/19

S h o w w o r k i n g s p l e a s e s i r

Answered by Rasheed.Sindhi last updated on 21/Sep/19

m^{6} + n^{6} + 375 m^{2} n^{2} = 1953125

\Rightarrow m^{6} + n^{6} + 3 m^{2} n^{2} (125) = {(125)}^{3}

C o m p a r e i t w i t h :

{(m^{2})}^{3} + {(n^{2})}^{3} + 3 m^{2} n^{2} (m^{2} + n^{2})

= {(m^{2} + n^{2})}^{3}

\Rightarrow m^{2} + n^{2} = 125

m = \sqrt{125 - n^{2}}

O n l y f o r n = 2, 11, 5, 10 m \in Z^{+}

H e n c e

T h e s o l u t i o n s a r e

(m, n) = (2, 11), (11, 2), (5, 10), (10, 5)

Commented by mr W last updated on 21/Sep/19

n i c e s o l u t i o n!

Commented by Rasheed.Sindhi last updated on 21/Sep/19

T h α n k s S i r!