Question

In the following equation, solve for x: $\sqrt{2}x-\sqrt{3}=\sqrt{5}$
(4 marks)

Answer 1

First we can add $\sqrt{3}$ to both sides:

$x \sqrt{2} = \sqrt{5} + \sqrt{3}$

Next we can divide both sides by $\sqrt{2}$:

$x = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{2} }$

Finally, we can rationalize the denominator by multiplying the numerator and denominator by $\sqrt{2}$:

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} }$

$\frac{ \sqrt{2}(\sqrt{5} + \sqrt{3}) }{ 2 }$

$x = \frac{ \sqrt{10} + \sqrt{6} }{ 2 }$