If we take three consecutive natural numbers, what is the relation between the product of the first and last, and the middle number?
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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
Step-by-step explanation:
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