Question 3:
Find two numbers whose sum is 27 and product is 182.
Answer:
Let the first number be x and the second number is 27 − x.
Therefore, their product = x (27 − x)
It is given that the product of these numbers is 182.
Therefore, x(27 – x) = 182
⇒ x2 – 27x + 182 = 0
⇒ x2 – 13x – 14x + 182 = 0
⇒ x(x – 13) –14 (x – 13) = 0
⇒ (x – 13) (x – 14) = 0
Either x – 13 = 0 or x − 14 = 0
i.e., x = 13 or x = 14
If first number = 13, then
Other number = 27 − 13 = 14
If first number = 14, then
Other number = 27 − 14 = 13
Therefore, the numbers are 13 and 14.
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