Discussion
If A.M. and G.M. of two numbers are 10 and 8 respectively, find the numbers.
Answer: A
Let the numbers be a and b. A.M. = \(\frac{a+b}{2} = 10 \Rightarrow a+b=20\). G.M. = \(\sqrt{ab} = 8 \Rightarrow ab=64\). We need two numbers whose sum is 20 and product is 64. The numbers are 4 and 16. We can solve this using the quadratic equation \(x^2 - (sum)x + (product) = 0 \Rightarrow x^2 - 20x + 64 = 0 \Rightarrow (x-4)(x-16)=0\).
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