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1. The roots of \(7x^2+x-5=0\) are a and b. Compute (a-4)(b-4).

 

2. The real numbers x and y are such that x + y = 4, x^2 + y^2 = 22, and x^4 = y^4 - 176 sqrt(7). Compute x-y.

 Jun 26, 2020
 #1
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1. (a - 4)(b - 4) = -17.

 

2. x - y = 12*sqrt(7).

 Jun 26, 2020
 #2
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1 .    a and b    =    -1/14 +- sqrt141 / 14    =    0.776739   and   −0.919596

             (via Quadratic Formula)

     so (a-4)(b-4) = 15.857

 Jun 26, 2020
edited by ElectricPavlov  Jun 26, 2020

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