SOLUTION: If x = (19 + 8√3)^(½) find (x⁴ - 6x³ - 2x² + 18x + 23)/(x² - 8x + 15)

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Question 1209552: If x = (19 + 8√3)^(½)
find (x⁴ - 6x³ - 2x² + 18x + 23)/(x² - 8x + 15)

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
If   x = (19 + 8√3)^(1/2),   find   .
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                        S T E P     b y     S T E P


(1)   = .

         To check and to prove, simply square right side.  You will get then  .



(2)  So, x = .  

         It implies  x-4 = ,  (x-4)^2 = 3,  x^2 - 8x + 16 = 3,  x^2 - 8x + 13 = 0.



(3)  Let's calculate the denominator  x^2 - 8x + 15.

         It is  x^2 -8x + 15 = (x^2 - 8x + 13) + 2.

         The part in parentheses is zero, so  the denominator  x^2 - 8x + 15  is simply  2.



(4)  In principle, the numerator can be calculated directly, but it is computationally boring procedure.

     It is simpler to perform a long division.

            = x^2 + 2x - 1 +  = 

         = x^2 + 2x - 1 +  = (x^2 + 2x - 1) + (19 - 10x) = x^2 - 8x + 18 = (x^2 - 8x + 13) + 5.



(5)  The value in the parentheses is zero, as we established above.

     So, we get the 



ANSWER.  If  x = (19 + 8√3)^(1/2),  then    is equal to 5.

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!






(I used a calculator to evaluate that one...!)





ANSWER: 5


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