Question

sum of the square of the two consecutive odd in natural numbers is greater than 8 times the sum by 2 find the number​

Answer 1

Let consecutive odd natural numbers be x, x+2

According to the question,

x^2+(x+2)^2=8(x+x+2)+2

x^2+x^2+4+4x=16x+16+2

2x^2+4x-16x=18-4

2x^2-12x-14=0

x^2-6x-7=0

x^2-7x+x-7=0

x(x-7)+1(x-7)=0

Now value of x=7

The two consecutive odd natural numbers are 7,9