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Find Two Consecutive Positive Odd Numbers, the Sum of Whose Squares is 74. - Mathematics

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Question

Find two consecutive positive odd numbers, the sum of whose squares is 74.

Solution

Let the consecutive positive odd numbers be x and x + 2.
From the given information,
x2 + (x + 2)2 = 74
2x2 + 4x + 4 = 74
2x2 + 4x – 70 = 0
x2 + 2x – 35 = 0
(x + 7)(x – 5) = 0
x = -7, 5
Since, the numbers are positive, so, x = 5.
Thus, the numbers are 5 and 7.

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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: 9 | Page no. 70
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Find Two Consecutive Positive Odd Numbers, the Sum of Whose Squares is 74. Concept: Quadratic Equations.
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