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The Sum of the Squares of Two Consecutive Positive Even Numbers is 52. Find the Numbers. - ICSE Class 10 - Mathematics

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Question

The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.

Solution

Let the consecutive positive even numbers be x and x + 2.
From the given information,
x2 + (x + 2)2 = 52
2x2 + 4x + 4 = 52
2x2 + 4x – 48 = 0
x2 + 2x – 24 = 0
(x + 6) (x – 4) = 0
x = -6, 4
Since, the numbers are positive, so x = 4.
Thus, the numbers are 4 and 6.

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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: 8
Solution The Sum of the Squares of Two Consecutive Positive Even Numbers is 52. Find the Numbers. Concept: Quadratic Equations.
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