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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 - Mathematics

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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+ y= 208 ..... (i)

y2 = 18x ..... (ii)

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

208 - x= 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.

 

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(A) | Q: 7 | Page no. 70
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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 Concept: Solutions of Quadratic Equations by Factorization.
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