sqrt(x^2 - 5) + sqrt(x - 2) = 3

asked by guest
on Oct 28, 2024 at 8:30 am



You asked:

Solve the equation \(\sqrt{{x}^{2} - 5} + \sqrt{x - 2} = 3\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= 3\\x &= - \frac{\sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}}{2} - \frac{61}{18 \sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}} - \frac{1}{3} + i \left(- \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}}{2}\right) \approx -3.1568773 + 1.8931105 i\\x &= - \frac{\sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}}{2} - \frac{61}{18 \sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}} - \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}}{2} + \frac{61 \sqrt{3}}{18 \sqrt[3]{\frac{2 \sqrt{1695}}{3} + \frac{881}{27}}}\right) \approx -3.1568773 -1.8931105 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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