Question

11)The sum of the the squares of consecutive natural numbers is 13. The quadratic

equation of this statement is

A) x
2 + x + 13 = 0 B) x
2 − x− 6 = 0

C) x

2 + x − 6 = 0 D) x

2 − x+ 25 = 0​

Answer 1

Explanation:

consecutive natural number means we take 2 number in a continues series

let first number be x

and another number be x+1

x²+(1+x) ²= 13

x²+x²+1²+2.1.x =13

2x²+1+2x=13

2x²+2x=13-1

2x²+2x=12

2x²+2x-12=0

x²+x-6=0 taking 2 common n divide to 0 which also give 0.

so required quadratic is

x²+x-6=0

Answer 2

Explanation Step-by-step

According to the question

The sum of the squares of consecutive numbers is 13.

let $x$ be the first number

then the next number = $x + 1$

now, according to the question;

⇒ $x^{2} + (x+1)^{2} = 13$

now, using the formula $(x+y)^{2} = x^{2} + y^{2} + 2xy$

⇒ $x^{2} + x^{2} + 1^{2} + 2x = 13$

⇒ $2x^{2} + 2x + 1 - 13 =0$

⇒ $2x^{2} + 2x- 12=0$

⇒ $2 ( x^{2} + x -6 ) = 0$ ( taking 2 common)

⇒$x^{2} +x-6=0$ ( when 2 is divided by 0, we get 0)

hence, the correct answer is $x^{2} + x - 6= 0$

#SPJ2