Question
Download Solution PDFIf AM and GM of two positive number a and b are 10 and 8 respectively. Find the numbers .
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If A is the arithmetic mean of numbers a and b and is given by ⇔ A = (a + b)/2
If G is the geometric mean of the numbers a and b and is given by ⇔ G = \(\rm \sqrt{ab}\)
Calculation:
Here AM = 10 and GM = 8
So,\(\rm\frac{a + b}{2}\) = 10
⇒ a + b = 20 ....(1)
Again , \(\rm \sqrt{ab}\) = 8
⇒ ab = 64 ....(2)
After solving both equation, we get a = 4, b = 16 or a = 16, b = 4
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