4 ms·

"Trying out numbers" seems like the simpler approach to me. You have to multiply four consecutive numbers to get 1680. One of them must be 7 (since 7 divides 16

"Trying out numbers" seems like the simpler approach to me. You have to multiply four consecutive numbers to get 1680. One of them must be 7 (since 7 divides 1680), one must be 5 or 10 for the same reason. That leaves only 3 possibilities, and you only have to check the middle one (5 x 6 x 7 x 8) since if the result too big or too small, you'll know which of the other two it is. OK - you weren't guaranteed the solution was an integer or even real, but you should strongly suspect there's a simple answer because you didn't get generic fourth-degree polynomials in your class. Depending on the class, you might be expected to find one, two or all four solutions - but once you have the first one the rest are much easier.

jusssi 5y ago
Following the procedure taught in class (and I'm quite sure they didn't teach "make a guess") is safer. When you show the correct procedure and fumble say, and addition, near the end, you'll still get almost full points. If you go off-road and get the wrong answer, it's up to how much the teacher likes you.
- dmurray 5y ago
  This doesn't line up with all the other problems, which reward having some insight as well as the concrete algebra/arithmetic skills to finish it out. If anything, your approach sounds more like what's expected in American schools: either you have been taught a foolproof way to solve problems matching Pattern X, or you stare slack jawed at the question paper thinking "I must have been absent the day they covered this question pattern". Exactly the opposite of the kind of thinking described in the article. Besides, as in another comment of mine on this page, there is no generic method your teacher could have taught you here that always works. (If you think so, please set the right hand side to 1681 and solve that version...). The principal method I was taught for solving cubics was to make a guess. Numerical methods came later.
  - andi999 5y ago
    Ok, only following procedure I also don't like..

jusssi 5y ago

Following the procedure taught in class (and I'm quite sure they didn't teach "make a guess") is safer. When you show the correct procedure and fumble say, and addition, near the end, you'll still get almost full points. If you go off-road and get the wrong answer, it's up to how much the teacher likes you.

dmurray 5y ago
This doesn't line up with all the other problems, which reward having some insight as well as the concrete algebra/arithmetic skills to finish it out. If anything, your approach sounds more like what's expected in American schools: either you have been taught a foolproof way to solve problems matching Pattern X, or you stare slack jawed at the question paper thinking "I must have been absent the day they covered this question pattern". Exactly the opposite of the kind of thinking described in the article. Besides, as in another comment of mine on this page, there is no generic method your teacher could have taught you here that always works. (If you think so, please set the right hand side to 1681 and solve that version...). The principal method I was taught for solving cubics was to make a guess. Numerical methods came later.
- andi999 5y ago
  Ok, only following procedure I also don't like..