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 , &#160; a &#62; b &#62; 0 , is five times their geometric mean, then a + b a - b is equal to:

Aicharya · Accepted Answer

Arithmetic Mean = a + b 2 Geometric Mean = a b &#8658; a + b 2 = 5 a b &#8658; a + b = 10 a b &#8658; ( a + b ) 2 = 100 a b &#8658; ( a - b ) 2 = ( a + b ) 2 - 4 a b = 96 a b Now, &#8658; a + b a - b = ( a + b ) 2 ( a - b ) 2 = 100 96 = 5 6 12

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

Solution

If the arithmetic mean of two numbers a and b , &#160; a &#62; b &#62; 0 , is five times their geometric…

Solution

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