SOLUTION: By using the expansion of (2+x)^4 and (2-x)^4, find the exact value of (2+√3)^4 + (2-√3)^4

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Question 1126798: By using the expansion of (2+x)^4 and (2-x)^4, find the exact value of (2+√3)^4 + (2-√3)^4
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
1--4--6--4--1
(2+x)^4=16+4(8x)+6(4x^2)+4(4x)+x^4=16+32x+24x^2+8x^3+x^4
(2-x)^4=16-32x+24x^2-8x^3+x^4
Add those two for 32+48x^2+2 x^4
let x=sqrt(3)
32+144+18=194
Let x=sqrt(3)
16+32sqrt(3)+72+24 sqrt(3)+9=97+56 sqrt(3) for the first one (positive coefficients)
16-32 sqrt(3)+72-24 sqrt(3)+9=97-56 sqrt(3)
sum is 194