Find the value of k if (frac{k}{sqrt{3} + sqrt{2}}) = k(sqrt{3 – 2})
-
A.
3 -
B.
2 -
C.
(sqrt{3}) -
D.
(sqrt 2)
Correct Answer: Option D
Explanation
(frac{k}{sqrt{3} + sqrt{2}}) = k(sqrt{3 – 2})
(frac{k}{sqrt{3} + sqrt{2}}) x (frac{sqrt{3} – sqrt{2}}{sqrt{3} – sqrt{2}})
= k(sqrt{3 – 2})
= k((sqrt{3} – sqrt{2}))
= k(sqrt{3 – 2})
= k(sqrt{3}) – k(sqrt{2})
= k(sqrt{3 – 2})
k2 = (sqrt{2})
k = (frac{2}{sqrt{2}})
= (sqrt{2})