Next, we will use the factored form of 2x² — 18 (of course according to the problem) to find 2 factors of 4982 such that the sum of these is greater than 100. This will explicitly give us (2, 2491) as one of the answers. It can be easily seen (1, 4982) also works here.
Now we are going to work out for the other answers. The intuitive idea here is to start with the equation
where x is strictly positive. There is a little problem here because we have wrote 4982 into exactly three factors, whereas the problem asks for two factors.
We wish to write 4982 into two factors. The trick is to multiply either (x - 3) or (x + 3) by the remaining factor, which is 2 so that 4982 will be finally in two factors.
Going back, we divide the equation by 2 to obtain
Luckily, the only factors in pairs besides (47, 53) of 2491 is only (1, 2491) which will give us (2, 2491) and (1, 4982) as answers, which is already mentioned above so we don't have to worry for other answers.
The factors in pair (47, 53) will give us the other two answers (47 × 2 = 94, 53) and (47, 53 × 2 = 106) using the aforementioned trick.
Answers & Comments
Answer:
We will first factorise 2x² — 18 here forcibly
Next, we will use the factored form of 2x² — 18 (of course according to the problem) to find 2 factors of 4982 such that the sum of these is greater than 100. This will explicitly give us (2, 2491) as one of the answers. It can be easily seen (1, 4982) also works here.
Now we are going to work out for the other answers. The intuitive idea here is to start with the equation
where x is strictly positive. There is a little problem here because we have wrote 4982 into exactly three factors, whereas the problem asks for two factors.
We wish to write 4982 into two factors. The trick is to multiply either (x - 3) or (x + 3) by the remaining factor, which is 2 so that 4982 will be finally in two factors.
Going back, we divide the equation by 2 to obtain
Luckily, the only factors in pairs besides (47, 53) of 2491 is only (1, 2491) which will give us (2, 2491) and (1, 4982) as answers, which is already mentioned above so we don't have to worry for other answers.
The factors in pair (47, 53) will give us the other two answers (47 × 2 = 94, 53) and (47, 53 × 2 = 106) using the aforementioned trick.
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