Solve the equation 10 + √(8) = \frac{6x}{\sqrt{2}} Give your answer in the form \( \frac{a}{b} \) where a and b are integers. - Edexcel - A-Level Maths Pure - Question 7 - 2014 - Paper 2

To eliminate the fraction, multiply each term by (\sqrt{2}):

[2\sqrt{2} \cdot \sqrt{2} = 6x - 10\sqrt{2}]

This simplifies to:

[4 = 6x - 10\sqrt{2}]

Now, rearranging to isolate x gives:

[6x = 4 + 10\sqrt{2}] [x = \frac{4 + 10\sqrt{2}}{6}]

This can be simplified further:

[x = \frac{2 + 5\sqrt{2}}{3}]

We want to express the answer in the form ( \frac{a}{b} ) where a and b are integers. Thus, we write:

[x = \frac{5\sqrt{2} + 2}{3}]

Here, ( a = 5) and ( b = 3).