$$\frac{3}{\sqrt{5}-\sqrt{2}}=0\sqrt{3}-b\sqrt{2}$$
$b=-\frac{\sqrt{10}}{2}-1\approx -2.58113883$
$$\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}=0\sqrt{3}-b\sqrt{2}$$
$$\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}}=0\sqrt{3}-b\sqrt{2}$$
$$\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{5-2}=0\sqrt{3}-b\sqrt{2}$$
$$\frac{3\left(\sqrt{5}+\sqrt{2}\right)}{3}=0\sqrt{3}-b\sqrt{2}$$
$$\sqrt{5}+\sqrt{2}=0\sqrt{3}-b\sqrt{2}$$
$$\sqrt{5}+\sqrt{2}=0-b\sqrt{2}$$
$$0-b\sqrt{2}=\sqrt{5}+\sqrt{2}$$
$$-\sqrt{2}b=\sqrt{2}+\sqrt{5}$$
$$\left(-\sqrt{2}\right)b=\sqrt{2}+\sqrt{5}$$
$$\frac{\left(-\sqrt{2}\right)b}{-\sqrt{2}}=\frac{\sqrt{2}+\sqrt{5}}{-\sqrt{2}}$$
$$b=\frac{\sqrt{2}+\sqrt{5}}{-\sqrt{2}}$$
$$b=-\frac{\sqrt{10}}{2}-1$$
Show Solution
Hide Solution
