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# 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 - ICSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Factorization

#### 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 = x2

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

∴ x2 + 18x = 208

⇒ x2 + 18x - 208 = 0

⇒ x2 + 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?

#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6A | Q: 7
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.
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