#### 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 smaller number be .x Then square of a larger number = 18x

Also, square of the smaller number = x^{2}

It is given that the sum of the square of the integers is 208.

∴ x^{2} + 18x = 208

⇒ x^{2} + 18x - 208 = 0

⇒ x^{2} + 26x - 8x - 208 = 0

⇒ x(x + 26) - 8(x + 26) = 0

⇒ (x + 26)(x - 8) = 0

x + 26 = 0

x = -26

or

x - 8 = 0

x = 8

But, the numbers are positive. Therefore x = 8

∴ Square of the large number = 18x = 18 x 8 = 144

∴ Large numbers are 8 and 12.

Is there an error in this question or solution?

Solution 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.