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Sum of real Roots (Posted on 2013-01-27) Difficulty: 3 of 5
What is the sum of the real roots of (2+(2+(2+x)2)2)2=2000.

No Solution Yet Submitted by Danish Ahmed Khan    
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No decimal fractions | Comment 5 of 6 |
Avoiding decimals....

(2 + (2 + (2 + x)2)2)2 = 2000

(2 + (2 + x)2)2  = sqrt(2000) 2             (+ve root only since LHS is +ve)

(2 + x)2 = sqrt(sqrt(2000) 2) 2           (+ve root only since LHS is +ve)

(2 + x)2 = k     say,

x2 + 4x + 4 k = 0

Quadratic equation: Sum of roots = -b/a  =  -4


Edited on January 29, 2013, 11:42 am
  Posted by Harry on 2013-01-29 11:40:59

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