27 lines
515 B
Markdown
27 lines
515 B
Markdown
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a + b + c = 1000, so what is abc?
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a pythagorean triplet must make a < b < c
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we know that:
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let x be the sum
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### LaTeX
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```
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c = x - (a + b) \newline
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a^2 + b^2 = (x - (a + b))^2 \newline
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a^2 + b^2 = a^2 + 2ab - 2ax + b^2 - 2bx + x^2 \newline
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2ab - 2ax - 2bx + x^2 = 0 \newline
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\newline
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2bx - 2ab = x^2 - 2ax \newline
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(\frac{x^2}{x}) - 2a = 2b - (\frac{2ab}{x}) \newline
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-2a = 2b - (\frac{2ab}{x}) - (\frac{x^2}{x}) \newline
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\newline
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a = \frac{2bx - x^2}{2x - 2b}
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```
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