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The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller these two numbers ?
Answer & Solution
Correct Answer:
Option
A
Let the numbers be x and (28 - x)
Then,
$$\eqalign{ & \Leftrightarrow x\left( {28 - x} \right) = 192 \cr & \Leftrightarrow {x^2} - 28x + 192 = 0 \cr & \Leftrightarrow \left( {x - 16} \right)\left( {x - 12} \right) = 0 \cr & \Leftrightarrow x = 16{\text{ or }}x = 12 \cr} $$
So, the numbers are 16 and 12
Then,
$$\eqalign{ & \Leftrightarrow x\left( {28 - x} \right) = 192 \cr & \Leftrightarrow {x^2} - 28x + 192 = 0 \cr & \Leftrightarrow \left( {x - 16} \right)\left( {x - 12} \right) = 0 \cr & \Leftrightarrow x = 16{\text{ or }}x = 12 \cr} $$
So, the numbers are 16 and 12
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