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Sum and Square Root Sum (Posted on 2010-09-25) Difficulty: 3 of 5
Determine all possible pair(s) (x,y) of real numbers that satisfy this set of equations:

x+y = 23, and:

√(x2 + 12*y) + √(y2 + 12*x) = 33

*** For an extra challenge, solve this puzzle without the aid of an online equation solver or a computer program.

No Solution Yet Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
analytical solution | Comment 1 of 3

x+y=23 thus y=23-x, substituting this into the second we get
(x-12x+276) + (x-34x+529) = 33 squaring both sides we get
2x-46x+805+2( (x-12x+276)*(x-34x+529) ) = 1089
(x-12x+276)*(x-34x+529) = (x-23x-142)
x^4-46x^3+1213x^2-15732x+146004=x^4-46x^3+245x^2+6532x+20164
thus
968x^2-2264x+125840=0
968(x^2-23x+130)=0
968(x-10)(x-13)=0
thus x=10 and y=13 or
x=13 and y=10
thus the only real solutions are
(10,13) and (13,10)


  Posted by Daniel on 2010-09-25 13:36:26
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