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April 18th, 2017, 02:15 PM   #1
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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.
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April 18th, 2017, 03:37 PM   #2
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There are numerous identities that use x and y. It's unclear what is expected.
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April 19th, 2017, 02:58 AM   #3
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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.
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April 19th, 2017, 02:12 PM   #4
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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 non-negative) 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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