the sum of the squares of two consecutive odd natural numbers is greater than 8 times their sum by 2.find the numbers.
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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
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
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