Find the value of x if (frac{sqrt{2}}{x + sqrt{2}}) = (frac{1}{x – sqrt{2}})
- A.
3(sqrt{2}) + 4 - B.
3(sqrt{2}) – 4 - C.
3 – 2(sqrt{2}) - D.
4 + 2(sqrt{2})
Correct Answer: Option A
Explanation
(frac{sqrt{2}}{x + 2}) = x – (frac{1}{sqrt{2}})
x(sqrt{2}) (x – (sqrt{2})) = x + (sqrt{2}) (cross multiply)
x(sqrt{2}) – 2 = x + (sqrt{2})
= x(sqrt{2}) – x
= 2 + (sqrt{2})
x ((sqrt{2}) – 1) = 2 + (sqrt{2})
= (frac{2 + sqrt{2}}{sqrt{2} – 1} times frac{sqrt{2} + 1}{sqrt{2} + 1})
x = (frac{2 sqrt{2} + 2 + 2 + sqrt{2}}{2 – 1})
= 3(sqrt{2}) + 4
There is an explanation video available below.