# If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometricmean, then $\frac{a+b}{a-b}$     is equal to: Option 1) Option 2) Option 3) Option 4)

N neha
S Shantanu

Valve surrounding opening of the coronary sinus is.........

A) eustachian valve    b)  thebasious valve

C)mitral valve               d)tricuspid  valve

S solutionqc

As learned in

Arithmetic mean of two numbers (AM) -

$A=\frac{a+b}{2}$

- wherein

It is to be noted that the sequence a, A, b, is in AP where, a and b are the two numbers.

and

Geometric mean of two numbers (GM) -

$GM= \sqrt{ab}$

- wherein

It is to be noted that a,G,b are in GP and a,b are two non - zero numbers.

If $\frac{a + b}{2} = 5 \sqrt{ab}$

$a + b = 10 \sqrt{ab}$

$\left ( a - b \right )^{2} = \left ( a + b \right )^{2} - 4ab$

=> $\left ( 10\sqrt{ab}\right )^{2} - 4ab = 100ab - 4ab = 96ab$

$a - b = 4\sqrt{6}\sqrt{ab}$

Therefore:

$\frac{a + b}{a - b} = \frac{10\sqrt{ab}}{4\sqrt{6}\sqrt{ab}} = 5 \frac{\sqrt{6}}{12}$

Option 1)

Option 2)

Option 3)

Option 4)

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