What number added to 1 gives its own square?

1.	What number added to 1 gives its own square?
Answer» Let the number be x x + 1 = x² x² - x - 1 = 0 \(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{1\pm \sqrt{1+4}}{2}\) \(=\frac{1\pm \sqrt{5}}{2}\) Numbers \(\frac{1+\sqrt{5}}{2},\frac{1-\sqrt{5}}{2}.\)

Answer»

Let the number be x

x + 1 = x²

x² - x - 1 = 0

\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{1\pm \sqrt{1+4}}{2}\) \(=\frac{1\pm \sqrt{5}}{2}\)

Numbers \(\frac{1+\sqrt{5}}{2},\frac{1-\sqrt{5}}{2}.\)

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What number added to 1 gives its own square?

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