Question

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

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