JEE Main 2017 · 8 Apr · Shift 1 · Mathematics Q68

MathematicsSingle correct+4 / -1Question 68 of 90

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then $\dfrac{a+b}{a-b}$ is equal to :

\dfrac{\sqrt6}2

\dfrac{3\sqrt2}4

\dfrac{7\sqrt3}{12}

\dfrac{5\sqrt6}{12}

Answer and worked solution

Official answer: D

Let $\sqrt{ab}=g$ , so $a+b=10g$ and $(a-b)^2=(a+b)^2-4ab=96g^2$ :
$\frac{a+b}{a-b}=\frac{10}{4\sqrt6}=\frac{5\sqrt6}{12}.$

JEE Main 2017 · 8 Apr · Shift 1, Mathematics question 68