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Find all pairs (a,b) of real numbers such that

a + b = 10

a^4 + b^4 = 2800

 Jul 22, 2022
 #1
avatar+124524 
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a + b = 10     →  b =  10 - a    (1)

a^4 + b^4 =  2800       (2)

 

Sub (1)   into (2) and we have that

 

a^4  + ( 10 - a)^4 =  2800

 

a^4 + a^4 - 40a^3 + 600a^2 -4000a + 10000 =  2800

 

2a^4  - 40a^3 + 600a^2 - 4000a - 7200 =  0

 

a^4 - 20a^3  + 300a^2 - 2000a - 3600  = 0

 

The  (real) solutions to this are

 

a ≈ 11.451   b ≈ -1.451

or

a  ≈ -1.451   b ≈ 11.451

 

 

cool cool cool

 Jul 23, 2022

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