Solve x = 2 + sqrt(5); x ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x=2+\sqrt{5}; x^{2}$$

Solve for x, y

$y=4\sqrt{5}+9\approx 17.94427191$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$y=\left(2+\sqrt{5}\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(2+\sqrt{5}\right)^{2}$.

$$y=4+4\sqrt{5}+\left(\sqrt{5}\right)^{2}$$

The square of $\sqrt{5}$ is $5$.

$$y=4+4\sqrt{5}+5$$

Add $4$ and $5$ to get $9$.

$$y=9+4\sqrt{5}$$

The system is now solved.

$$x=2+\sqrt{5}$$ $$y=9+4\sqrt{5}$$