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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.

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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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