Question

Solve:
Example 8. The sum of squares of two positive integers is 208. If the square of the larger
number is 18 times the smaller number, find the numbers.

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Answer 1

Step-by-step explanation:

hope this answer helps you.

Let the two numbers be x and y, y being the bigger number. From the given information,

x2 + y2 = 208

y2 = 18x

From (i), we get y2 = 208 − x2. Putting this in (ii), we get,

208 − x2 = 18x

⇒ x2 + 18x − 208 = 0

⇒ x2 + 26x – 8x − 208 = 0

⇒ x(x + 26) − 8(x + 26) = 0

⇒ (x − 8)(x + 26) = 0

⇒ x can't be a negative number, hence x = 8

⇒ Putting x = 8 in (ii), we get y2 = 18 x 8 = 144

⇒ y = 12,

since y is a positive integer Hence, the two numbers are 8 and 12.

Answer 2

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Let the two numbers be x and y, y being the bigger number. From the given information,

x2 + y2 = 208

y2 = 18x

From (i), we get y2 = 208 − x2. Putting this in (ii), we get,

208 − x2 = 18x

⇒ x2 + 18x − 208 = 0

⇒ x2 + 26x – 8x − 208 = 0

⇒ x(x + 26) − 8(x + 26) = 0

⇒ (x − 8)(x + 26) = 0

⇒ x can't be a negative number, hence x = 8

⇒ Putting x = 8 in (ii), we get y2 = 18 x 8 = 144

⇒ y = 12,

since y is a positive integer Hence, the two numbers are 8 and 12.