Question

Let two positive intigers be such that their sum is 9 and the sum of their fourth powers is 2417. Find the two numbers?

Answer 1

@Arnab09 @yash2651995

Answer 2

\( \color{Black}{\Rightarrow a + b = 9 }\)

\( \color{Black}{\Rightarrow a^4 + b^4 = 2417 }\)

Although you may attempt a trial and error here.

Answer 3

this doesnt seem easy lol

Answer 4

8,1 ; 7,2 ; 3,6 ; 4,5

Answer 5

Check if any of em satisfy the second equation.

Answer 6

saw one :D

Answer 7

Yes... I got it ;D

Answer 8

Go put these in your calculator.

\( \color{Black}{\Rightarrow 8^4 + 1^4 }\)

\( \color{Black}{\Rightarrow 7^4 + 2^4 }\)

\( \color{Black}{\Rightarrow 6^4 + 3^4 }\)

\( \color{Black}{\Rightarrow 5^4 + 4^4 }\)

Answer 9

\[(a+b)^{4}= a ^{4}+b ^{4}+4(ab)(a+b)+6(ab)^{2}\]
find (ab) from here ..
then put it in \[(a-b)^{2}=(a+b)^{2}-4(ab)\]
then find a-b
use a+b=9 and a-b= ..what ever you get.. to find a and b

Answer 10

ab will be positive..^

Answer 11

your formulla is wrong @yash2651995 please recheck

Answer 12

ya.. let me correct it..

Answer 13

formulla is (a+b)^4 = a^4 + 4a^3 b + 6a^2 b^2 + 4ab^3 + b^4
=> a^4 + b^4 + ab ( 4a^2 + 4b^2 + 6ab)

Answer 14

and a^2+ b^2 = 81 -2ab
now you can make this subsn and this should just do it

Answer 15

\[(a+b)^{4}=a ^{4}+b ^{4}+4ab(a+b)^{2}-2(ab)^{2}\]

Answer 16

yep..same thing

Answer 17

ab=14 or 148..

Answer 18

a-b=5

Answer 19

a=7 b=2

Answer 20

or a=2 b=7