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The Sum of the Squares of Two Consecutive Odd Numbers is 394. Find the Numbers. - CBSE Class 10 - Mathematics

ConceptSolutions of Quadratic Equations by Completing the Square

Question

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

Solution

Let one of the number be x then the other number be x + 2.

Then according to question,

$x^2 + \left( x + 2 \right)^2 = 394$

$\Rightarrow x^2 + x^2 + 4x + 4 = 394$

$\Rightarrow 2 x^2 + 4x - 390 = 0$

$\Rightarrow x^2 + 2x - 195 = 0$

$\Rightarrow x^2 + 15x - 13x - 195 = 0$

$\Rightarrow x(x + 15) - 13(x + 15) = 0$

$\Rightarrow (x - 13)(x + 15) = 0$

$\Rightarrow x - 13 = 0 \text { or } x + 15 = 0$

$\Rightarrow x = 13 \text { or } x = - 15$

Since, x being an odd number,

Therefore, x = 13.

Then another number will be $x + 2 = 13 + 2 = 15$

Thus, the two consecutive odd numbers are 13 and 15.

Is there an error in this question or solution?

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Solution The Sum of the Squares of Two Consecutive Odd Numbers is 394. Find the Numbers. Concept: Solutions of Quadratic Equations by Completing the Square.
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