Question

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

Answer 1

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Answer 2

Answer:

$13 \: \: and \: \: 15$

Step-by-step explanation:

$let \: \: numbers \: \: be \: \: x \:, \: (x + 2)$

${x}^{2} + {(x + 2)}^{2} = 394$

${x}^{2} + {x}^{2} + 4 + 4x = 394$

$2 {x}^{2} + 4x + 4 = 394$

$2( {x}^{2} + 2x + 2) = 394$

${x}^{2} + 2x + 2 = 197$

${x}^{2} + 2x - 195 = 0$

${x}^{2} + 15x - 13x - 195 = 0$

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

$(x + 15)(x - 13)$

$x = 13$

$x + 2 = 15$

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