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