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beks73 [17]
2 years ago
5

PLEASE HELP ASAP Prove that x+a is a factor of (x+a)^5 + (x+c)^5 + (a-c)^5

Mathematics
1 answer:
Brums [2.3K]2 years ago
6 0

P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5

If x+a is a factor of P(x), then -a is a root of P(x).

Therefore

(-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0

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Tim was given a large bag of sweets and ate one third of the sweets before stopping as he was feeling sick. The next day he ate
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Answer: In the beginning he was given 27 sweets.

Step-by-step explanation: The most logical thing to do is to solve it backwards, that is, from what he had at the end of the third day up till the beginning of the first day.

On the third day he ate one-third and had 8 sweets left over. To determine how many he started with on the third day, let the total on day three be called a. If one-third of a is eaten, then the left over which is two-thirds is 8. That is;

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Let the number of sweets he had on day two be called b. If he ate one-third of b and he had 12 left over, then the two-thirds left over is 12 and we now have;

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By cross multiplication we now have

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b = 18

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