Question

5) Three consecutive natural numbers are
such that adding the square of the
smallest number to the product of the
other two numbers, the result is 67.
We want to find those three consecutive
natural numbers​

Answer 1

Answer:

Let the number be x−1,x.x+1

Given

x

2

−[(x+1)

2

−(x−1)

2

]=60

x

2

−[(x+1)

2

−(x−1)

2

]+60

x

2

=4x+60

⇒ x

2

−4x−60=0

⇒ x

2

−10x+6x−60=0

x(x−10)+6(x−10)=0

(x+6)(x−10)=0

⇒ x=6,10

∴ The numbers are 9,10,11