Moderate -0.8 This is a straightforward surd manipulation question requiring simplification of √8 and rationalization of the denominator, followed by solving a linear equation. It's easier than average as it involves only routine algebraic techniques with no problem-solving insight needed, though it requires more steps than the most basic index law recall questions.
5. Solve the equation
$$10 + x \sqrt { 8 } = \frac { 6 x } { \sqrt { 2 } }$$
Give your answer in the form \(a \sqrt { } b\) where \(a\) and \(b\) are integers.
For multiplying both sides by \(\sqrt{2}\) – allow a slip e.g. \(\sqrt{2}x\sqrt{8}+10=\frac{6x}{\sqrt{2}}\times\sqrt{2}\) or \(\sqrt{2}\times10+x\sqrt{8}=\frac{6x}{\sqrt{2}}\times\sqrt{2}\), where one term has an error. NB \(x\sqrt{8}+10=6x\sqrt{2}\) is M0
A1: correct equation in \(x\) with no fractional terms e.g. \(x\sqrt{16}+10\sqrt{2}=6x\). M1: attempt to solve linear equation producing answer of form \(a\sqrt{2}\) or \(a\sqrt{50}\). A1: \(5\sqrt{2}\) oe (accept \(1\sqrt{50}\))
Method 2:
Answer
Marks
Guidance
Answer/Working
Mark
Guidance
\(2\sqrt{2}x + 10 = 3\sqrt{2}x\)
M1, A1
M1: writing \(\sqrt{8}\) as \(2\sqrt{2}\) or \(\frac{6}{\sqrt{2}}\) as \(3\sqrt{2}\). A1: correct equation with no fractional terms e.g. \(2\sqrt{2}x+10=3\sqrt{2}x\) or \(x\sqrt{8}+10=3\sqrt{2}x\)
5. Solve the equation
$$10 + x \sqrt { 8 } = \frac { 6 x } { \sqrt { 2 } }$$
Give your answer in the form $a \sqrt { } b$ where $a$ and $b$ are integers.\\
\hfill \mbox{\textit{Edexcel C1 2014 Q5 [4]}}