Question

The sum of the squares of two positive integer is 208. if the square of the larger number is 18 times the smaller number find the numbers.





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Answer 1

Let the smaller number be x. Then,

Square of larger number = 18x

Square of the smaller number = x^2

Therefore,

x^2+18x=208

x^2+18x−208=0

(x+26)(x−8)=0

x=8,−26

But, the numbers are positive.

So, x=8

Hence, the numbers are 8 and 12.

Answer 2

Answer:

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

x2 + y2 = 208 (i)

y2 = 18x (ii)

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.

Explanation:

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