Question

If the arithmetic mean of two numbers a and b ,a>b>0 is five times geometric mean then

Answer 1

From the information we are given:

1/2(a+b)=5√ab

Multiply both sides by 2 to get:

a+b=10√ab

Square both sides to get:

(a+b)2=a2+2ab+b2=100ab

Subtract 4ab from both ends to get:

(a−b)2=a2−2ab+b2=96ab

So:

(a+b/a−b)2=100ab/96ab=25/24=5square⋅6/12square9=(5√612)square

So since a>b we can take the positive square root to find:

a+b/a−b=5√612

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Answer 2

Answer:

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