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प्रश्न
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
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उत्तर
Let the greater number be x and smaller number be y. Then, according to given information, we have
x2 – y2 = 180 ...(i)
And y2 = 8x ...(ii)
From equations (i) and (ii), we get
x2 – 8x – 180 = 0
⇒ x2 – 18x + 10x – 180 = 0
⇒ x(x – 18) + 10(x – 18) = 0
⇒ (x – 18)(x + 10) = 0
⇒ x = 18 ...[∵ x ≠ – 10, if x = –10, then y2 = –80 not possible]
Now, from equation (ii),
y2 = 8 × 18 = 144
⇒ y = ± 12
So, the two numbers are 18 and 12 or 18 and –12.
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