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प्रश्न
The sum of two numbers is 34. If 3 is subtracted from one number and 2 is added to another, the product of these two numbers becomes 260. Find the numbers.
उत्तर
Let the numbers be x and y.
Then, according to given condition, we have
x + y = 34 ...(i)
and (x – 3)(y + 2) = 260 ...(ii)
On substituting the value of y from equation (i) in equation (ii), we get
(x – 3)(34 – x + 2) = 260 ...[∵ y = 34 – x]
⇒ (x – 3)(36 – x) = 260
⇒ 36x – x2 – 108 + 3x = 260
⇒ x2 – 39x + 368 = 0
⇒ x2 – (16x + 23x ) + 368 = 0
⇒ x2 – 16x – 23x + 368 = 0
⇒ x(x – 16) – 23(x – 16) = 0
⇒ (x – 16)(x – 23) = 0
⇒ x = 16 or x = 23
When x = 16, then y = 34 – 16 = 18
When x = 23, then y = 34 – 23 = 11
So, the numbers are 16, 18 or 23, 11.
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