The sum of squares of two consecutive odd num | vedclass

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(B) Let the two consecutive odd numbers be $x$ and $x + 2$.According to the problem,the sum of their squares is $514$:$x^2 + (x + 2)^2 = 514$$x^2 + x^

Vedclass · Accepted Answer

$15, 17$

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(B) Let the two consecutive odd numbers be $x$ and $x + 2$.According to the problem,the sum of their squares is $514$:$x^2 + (x + 2)^2 = 514$$x^2 + x^2 + 4x + 4 = 514$$2x^2 + 4x + 4 = 514$$2x^2 + 4x - 510 = 0$Dividing by $2$:$x^2 + 2x - 255 = 0$Factoring the quadratic equation:$x^2 + 17x - 15x - 255 = 0$$x(x + 17) - 15(x + 17) = 0$$(x - 15)(x + 17) = 0$Since the numbers are positive,$x = 15$.The two numbers are $15$ and $15 + 2 = 17$.

The sum of squares of two consecutive odd numbers is $514$. Find those numbers.

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