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April 18th, 2017, 02:15 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 507 Thanks: 74  How Do You Write A Generic Form Of This Equation?
My dad gave me the problem: Square root of (x + 15) + Square root of x = 15 x = 49, with the equation simplifying to 8 + 7 = 15. In general, the constant term, which in this case is 15 is 2*(square root of x) + 1. If the constant term decreased by 2 to 13, x would decrease by 13 to the next lower square number. If you call y the constant term, write an identity using x and y. 
April 18th, 2017, 03:37 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 16,944 Thanks: 1255 
There are numerous identities that use x and y. It's unclear what is expected.

April 19th, 2017, 02:58 AM  #3 
Member Joined: Mar 2017 From: Tasmania Posts: 36 Thanks: 2 
assuming x is still 49 the equation is y = real answer (in this case 15) + (x(real answer)) (0.062) y= 15+(x  15)(0.059) (0.059) to get this just take 2 equations then find difference of y Last edited by Posher; April 19th, 2017 at 03:02 AM. 
April 19th, 2017, 02:12 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 16,944 Thanks: 1255 
That doesn't make sense to me. The problem seems to say that y = 2√x + 1 is what in general makes the original equation true. They may be hinting at the identity x + y ≡ (√x + 1)², because that's equivalent (if x is nonnegative) to √(x + y) ≡ √x + 1, which is equivalent to √(x + y) + √x ≡ 2√x + 1, which is equivalent to the original equation if y = 2√x + 1. However, that makes no use of the remarks about decreasing the value of y, which themselves require that x is a perfect square, so that "the next lower square number" (than x) is meaningful. 

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