the sum of the squares of three consecutive natural numbers is 2030. Then what is the middle number?

Question

options

 

A) 27

 

B) 26

 

C) 25

 

D) 28

 

E) 24

Answer 1

Let

1st no. = x

2nd no. =x+1

3rd no. = x+2

 

x^2+(x+1)^2+(x+2)^2=2030

 

x^2 +x^2+2x+1 +x^2+4x +4 =2030

3x^2 +6x+5=2030

 

3x^2+6x -2025 =0  

 

divide equation with 3

 

x^2+2x -675 =0

(x+27)(x-25)=0

x=-27 or x=25

 

x=-27 is not natural number

 

so x= 25

 

1st no. = x  = 25
2nd no. =x+1 = 26
3rd no. = x+2 = 27

 

middle number is 26