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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
Question 7
Solve the equation 10 + √8 = \frac{6x}{\sqrt{2}} Give your answer in the form \( \frac{a}{b} \) where a and b are integers.
Worked Solution & Example Answer: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
Step 1
Multiply both sides by \( \sqrt{2} \)
Answer
Multiplying both sides by ( \sqrt{2} ) gives:
( \sqrt{2} \cdot (10 + \sqrt{8}) = 6x )
This simplifies to:
( 10\sqrt{2} + \sqrt{8} \cdot \sqrt{2} = 6x )
Recognizing that ( \sqrt{8} \cdot \sqrt{2} = \sqrt{16} = 4 ), we rewrite the equation as:
( 10\sqrt{2} + 4 = 6x )
Step 2
Step 3
Expressing in the required form
Answer
To express the answer in the form ( \frac{a}{b} ), we have:
( a = 5\sqrt{2} + 2 ) ( b = 3 )
We note that the required form is achieved by recognizing that:
( x = \frac{5\sqrt{2}}{3} + \frac{2}{3} )
Thus, the final answer is ( \frac{5\sqrt{2}}{3} + \frac{2}{3} ).