If the arithmetic mean of two numbers a and b, a b 0, is five times their geometric mean, then (a + b/a - b) is equal to :

Question

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then (a + b/a - b) is equal to : (A) (√6/2) (B) (3√2/4) (C) (7√3/12) (D) (5√6/12)

Tardigrade Admin · Accepted Answer

(a+b/2) = 5√ab (a+b/√ab) = 10 ∴ (a/b) = (10+√96/10-√96) = (10+4√6/10-4√6) Use C and D (a+b/a-b) = (20/8√6) = (5/2√6) = (5√6/12)

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

$\frac{6}{2}$

$\frac{3 2}{4}$

$\frac{7 3}{12}$

$\frac{5 6}{12}$

$\frac{a + b}{2} = 5 ab$
$\frac{a + b}{ab} = 10$
$∴ \frac{a}{b} = \frac{10 + 96}{10 - 96} = \frac{10 + 4 6}{10 - 4 6}$
Use C and D
$\frac{a + b}{a - b} = \frac{20}{8 6} = \frac{5}{2 6} = \frac{5 6}{12}$

Q. If the arithmetic mean of two numbers a and b, a>b>0, is five times their geometric mean, then a−ba+b​ is equal to :

26​​

432​​

1273​​

1256​​