Pls give the solution | Mathematics | Page 1

frigid fable Dec 30, 2024, 3:31 AM

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Can anyone tell me some resources from where I can practice these sort of question

vernal houndBOT Dec 30, 2024, 3:31 AM

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marsh tartan Dec 30, 2024, 9:30 AM

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(x + 2y)^2 + 2x + 5y + 9 = (y + z)^2
(x + 2y)^2 + 2(x + 2y) + y + 9 = (y + z)^2
(x + 2y)^2 + 2(x + 2y) + 1 + y + 8 = (y + z)^2
(x + 2y + 1)^2 + y + 8 = (y + z)^2

If y + 8 is a perfect square, the equation looks like a^2 + b^2 = c^2.

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got it?

hybrid carbon Dec 30, 2024, 9:45 AM

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marsh tartan (x + 2y)^2 + 2x + 5y + 9 = (y + z)^2 (x + 2y)^2 + 2(x + 2y) + y + 9 = (y + z)^2 ...

That was crazy but what after?

marsh tartan Dec 30, 2024, 9:46 AM

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a = 4, b = 3, c = 5 → y = 1. x = 1. z = 4

hybrid carbon Dec 30, 2024, 9:46 AM

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5 12 13?

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Oh wait question is to at least find 1 solution?

frigid fable Dec 30, 2024, 11:19 AM

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why y + 8 will be a perfect square?

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can you pls explain this a bit

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I got the rest

hybrid carbon Dec 30, 2024, 11:20 AM

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Was question to find all solutions?

frigid fable Dec 30, 2024, 11:26 AM

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The question was just the ss I sent

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nothing else was written

marsh tartan Dec 30, 2024, 2:32 PM

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no like if it becomes a perfect square, as we assume it, to it takes the form of a quadratic

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im so sorry for the late revert

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we assume that it becomes a quadratic else the equation wouldnt have positive integers

#Pls give the solution