SOLUTION: If x= 1+ sqrt2 + sqrt3, then the value of 2x^4-8x^3-5x^2+26x-28

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Question 650728: If x= 1+ sqrt2 + sqrt3, then the value of 2x^4-8x^3-5x^2+26x-28
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
x2 = (1+Ö2+Ö3)2 = 6+2Ö2+2Ö3+2Ö6
x3 = (1+Ö2+Ö3)3 = 16+14Ö2+12Ö3+6Ö6
x4 = (1+Ö2+Ö3)4 = 80+48Ö2+40Ö3+32Ö6

 2x4 =  2(1+Ö2+Ö3)4 = 160+ 96Ö2+80Ö3+64Ö6
-8x3 = -8(1+Ö2+Ö3)3 =-128-112Ö2-96Ö3-48Ö6
-5x2 = -5(1+Ö2+Ö3)2 = -30- 10Ö2-10Ö3-10Ö6
+26x = 26(1+Ö2+Ö3) =  26+ 26Ö2+26Ö3
-28                = -28 
------------------------------------
                   =   0+  0Ö2+ 0Ö3+ 6Ö6

Answer = 6Ö6

Edwin