SOLUTION: fiND THE VALUE OF: {(A^2-AB+B^2)/(A^2+AB+B^2)} IF A=(1-7^1/2)/(1+7^1/2) AND B=(1+7^1/2)/(1-7^1/2).

Algebra ->  Triangles -> SOLUTION: fiND THE VALUE OF: {(A^2-AB+B^2)/(A^2+AB+B^2)} IF A=(1-7^1/2)/(1+7^1/2) AND B=(1+7^1/2)/(1-7^1/2).      Log On


   

Question 1047301: fiND THE VALUE OF: {(A^2-AB+B^2)/(A^2+AB+B^2)} IF A=(1-7^1/2)/(1+7^1/2) AND B=(1+7^1/2)/(1-7^1/2).
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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Finf the value of: {(A^2-AB+B^2)/(A^2+AB+B^2)} IF A=(1-7^1/2)/(1+7^1/2) AND B=(1+7^1/2)/(1-7^1/2).
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1.  Notice that AB = 1.  Therefore, 

    %28A%5E2-AB%2BB%5E2%29%2F%28A%5E2%2BAB%2BB%5E2%29 = %28%28A-B%29%5E2+%2B+AB%29%2F%28%28A%2BB%29%5E2+-+AB%29 = %28%28A-B%29%5E2+%2B1%29%2F%28%28A%2BB%29%5E2+-+1%29.


2.  Next,  A+B = -1%2F3.   A-B = sqrt%287%29%2F12.   It is pure arithmetic.

3.  Finally, your expression is  %28%28sqrt%287%29%2F12%29%5E2%2B1%29%2F%28%28-1%2F3%29%5E2+-1%29 = %287%2F144%2B1%29%2F%281%2F9-1%29 = %28%28151%2F144%29%29%2F%28%28-1%2F8%29%29 = -151%2F18.