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:, 7 3 12, 3 2 4, 6 2, 5 6 12

MARKS App · Accepted Answer

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

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