Eric Nicholas K's answer to haha's Secondary 2 Maths Singapore question.
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Here are my explanations for the first question in the photo.
I have listed out the list of perfect squares of the first twenty numbers on top and the same numbers added by 1 below.
Look at the list of numbers below. The terms n2 + 1 and (n + 1)^2 + 1 appear next to each other in the list, because n and n + 1 are consecutive terms.
If you observe any two consecutive numbers in the list, we see that terms appear as odd and even alternately, so 2 cannot be common divisors.
From the ones which I placed in red rectangles, you can see that 5 can be common divisors of the two expressions (depending on n of course).
By observation, none of the numbers are divisible by 3, 7, 11 and so on.
Hence, the possible values of d are 1, 5 and their negatives (-1 and -5).
I have listed out the list of perfect squares of the first twenty numbers on top and the same numbers added by 1 below.
Look at the list of numbers below. The terms n2 + 1 and (n + 1)^2 + 1 appear next to each other in the list, because n and n + 1 are consecutive terms.
If you observe any two consecutive numbers in the list, we see that terms appear as odd and even alternately, so 2 cannot be common divisors.
From the ones which I placed in red rectangles, you can see that 5 can be common divisors of the two expressions (depending on n of course).
By observation, none of the numbers are divisible by 3, 7, 11 and so on.
Hence, the possible values of d are 1, 5 and their negatives (-1 and -5).
Date Posted:
5 years ago
thank you so much!
Does anyone know how to solve questions 4 and 5?
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