SOLUTION: (2x+5)^4+(2x+1)^4=82 [Hint: Put (2x+3)=y]

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Question 1031967: (2x+5)^4+(2x+1)^4=82 [Hint: Put (2x+3)=y]
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%2B5%29%5E4%2B%282x%2B1%29%5E4=82 [Hint: Put (2x+3)=y]

Using the hint 2x+3=y, then 2x=y-3.  
Substitute y-3 for 2x:

%28y-3%2B5%29%5E4%2B%28y-3%2B1%29%5E4=82

%28y%2B2%29%5E4%2B%28y-2%29%5E4=82

Multiply that out and collect terms:

2y%5E4%2B48y%5E2%2B32=82

2y%5E4%2B48y%5E2-50=0

Divide through by 2

y%5E4%2B24y%5E2-25=0

%28y%5E2-1%29%28y%5E2%2B25%29=0

%28y-1%29%28y%2B1%29%28y%5E2-25i%5E2%29=0

%28y-1%29%28y%2B1%29%28y-5i%29%28y%2B5i%29=0

y=1, y=-1, y=5i, y=-5i

Since 2x+3=y

2x+3=1, 2x+3=-1, 2x+3=5i, 2x+3=-5i

2x=-2, 2x=-4, 2x=-3+5i, 2x=-3-5i

x=-1, x=-2, x=-3/2+5/2i, x=-3/2-5/2i

Edwin