The sum of squares of two consecutive odd num | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$15, 17$

Vedclass · Answer

(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.

Similar Questions

Which of the following is a quadratic equation in one variable?

If the value of the discriminant of the quadratic equation $x^{2} + \sqrt{2}x + 2 = 0$ is .... .

Which constant should be added and subtracted to solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square?

Solve the following equation using the method of factorization: $\frac{x^{2}-1}{x^{2}+1}=\frac{7}{9}$

Solve the following quadratic equation using the method of factorization: $x^{2} + 5x - 66 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module