#### Question

The sum of the squares of two positive integers is 208. If the square of the large number is 18 times the smaller. Find the numbers.

#### Solution

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

x^{2 }+ y^{2 }= 208 ..... (i)

y^{2} = 18x ..... (ii)

From (i), we get y^{2}=208 - x^{2}. Putting this in (ii), we get,

208 - x^{2 }= 18x

x^{2} + 18x - 208 = 0

x^{2} + 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 y^{2} = 18 x 8=144

y = 12, since y is a positive integer

Hence, the two numbers are 8 and 12.

Is there an error in this question or solution?

Advertisement

Advertisement

The Sum of the Squares of Two Positive Integers is 208. If the Square of the Large Numbr is 18 Times the Smaller. Find the Numbers Concept: Solutions of Quadratic Equations by Factorization.

Advertisement