There are positive integers m and n such that m 2 </msup> &#x2212; n = 32 and

studovnaem4z6

studovnaem4z6

Answered question

2022-05-13

There are positive integers m and n such that m 2 n = 32 and
m + n 5 + m n 5
is a real root of the polynomial
x 5 10 x 3 + 20 x 40
Find m+n

Answer & Explanation

radcas87gex5r

radcas87gex5r

Beginner2022-05-14Added 13 answers

Your second idea is better
( a + b ) 5 = a 5 + b 5 + 5 a b ( a 3 + b 3 ) + 10 a 2 b 2 ( a + b )
So
x 5 = 2 m + 10 ( a + b ) ( ( a + b ) 2 6 ) + 40 ( a + b )
or
x 5 + 2 m + 10 x 3 60 x + 40 x
so
x 5 10 x 3 + 20 x 2 m = 0
and thus m = 20

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