Question

Three consecutive positive integers are raised to the
first, second and third powers respectively and then
added. The sum so obtained is a perfect square, whose
square root equals the total of the three original inte-
gers. Which of the following best describes the mini-
mum, say m, of these three integers?
(a) 1 <= m <= 3
(b) 4 <= m < = 6
(c) 7 <= m <= 9
(d) 10 <= m <= 12
(e) 13 <= m <= 15​

Answer 1

Answer:

Let the three integers be m−1,m,m+1

As given,

m−1+m

2

+(m+1)

3

=(m−1+m+m+1)

2

m−1+m

2

+m

3

+1+3m

2

+3m=9m

2

m

3

−5m

2

+4m=0

m(m

2

−5m+4)=0

m(m−1)(m−4)=0

m=0,1,4

m cannot be 0 o 1 else the smallest number will be either -1 or 0 which is not possible.

Hence, m=4

and smallest number then is 3

Thus correct answer is 1≤m≤3

hope it helps

please follow me