My Math Forum Needs help with this text book question

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 January 24th, 2014, 11:25 AM #1 Newbie   Joined: Jan 2014 Posts: 7 Thanks: 0 Needs help with this text book question A student writes down the following incomplete piece of work. x2 - 27x - 0 Adding 27x to both sides x2 - 27x Divide both sides by x x - 27 (a) Substitute x = 27 into the equation x2 ? 27x = 0, and explain why this shows that x = 27 is indeed a solution of the equation. [2] (b) Write out a complete solution of the equation x2 ? 27x = 0. [2] (c) Explain, as if directly to the student, why their working is incorrect. A quick response to the above would be great.
January 25th, 2014, 11:28 PM   #2
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Re: Needs help with this text book question

Quote:
 Originally Posted by roberto.salamanca A student writes down the following incomplete piece of work. x2 - 27x - 0 Adding 27x to both sides ... (c) Explain, as if directly to the student, why their working is incorrect. A quick response to the above would be great.
A quick response would be that there are no "both sides" in x2 - 27x - 0. By the way, in plain text, it is customary to write x^2 for $x^2$.

What exactly do you need help with? Substituting x = 27 into x^2 ? 27x = 0?

 January 26th, 2014, 10:58 AM #3 Newbie   Joined: Jan 2014 Posts: 7 Thanks: 0 Re: Needs help with this text book question I am not even sure myself as the question are from the text book and dont quite get it MYSELF . I also need to explain why the students workings are incorrect ?
January 26th, 2014, 11:39 AM   #4
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Re: Needs help with this text book question

Quote:
 Originally Posted by roberto.salamanca A student writes down the following incomplete piece of work. x2 - 27x - 0 Adding 27x to both sides x2 - 27x Divide both sides by x x - 27
First, I think the student's work is actually

x² - 27x = 0 Adding 27x to both sides
x² = 27x Divide both sides by x
x = 27

The problem with this is that the original equation has two roots: x = 27 and x = 0, as can be verified by plugging these values in. On the other hand, the student found only one root: x = 27.

A proper solution of an equation must consist of a series of statements that are equivalent. This means that any x satisfies one statement iff it satisfies another. For example, the first two lines

(1) x² - 27x = 0
(2) x² = 27x

are indeed equivalent: if an x satusfies (1), then it satisfies (2) and vive versa. However, (2) and the third line:

(3) x = 27

are not equivalent because x = 0 satisfies (2) but not (3). We could say that (3) implies (2) but not vice versa. The correct way to solve (1) is to say

(4) x(x - 27) = 0

Since a product is zero iff at least one of the factors is zero, (4) is equivalent to

x = 0 or x - 27 = 0

which in turn is equivalent to

x = 0 or x = 27.

January 29th, 2014, 12:04 PM   #5
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Re: Needs help with this text book question

I understand now, thank so very much for helping me on this.

Been going through my text book and now come against another struggle, trigonometry

I have attached some questions that my tutor has tried to explain but i still dont get it, could you talk me through it step by step?

Thanks you again,
Rob

The file is attached
Attached Files
 Trigonometry.docx (114.9 KB, 25 views)

 January 29th, 2014, 12:55 PM #6 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 Re: Needs help with this text book question If the new question(s) are unrelated to the one in the OP, I recommend starting a new thread.
 January 30th, 2014, 10:47 AM #7 Newbie   Joined: Jan 2014 Posts: 7 Thanks: 0 Re: Needs help with this text book question I understand will do in the future, but was hoping you could help with this? Thank you
 January 31st, 2014, 07:27 AM #8 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 Re: Needs help with this text book question Concerning problem (a). Angles GDE and CGD are alternating and thus equal. Angles GED, BGC and AFG are corresponding and thus are also equal. Finally, angles AGF and CGD are vertical and therefore equal. So, in triangles AGF and GDE there are two equal angles, and since the sum of all angles in a triangle is 180 degrees, the third angles are also equal. Therefore, triangles AGF and GDE are similar by three equal angles.
 January 31st, 2014, 10:45 AM #9 Senior Member   Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108 Re: Needs help with this text book question Concerning problem (b)(i): DE/AC = FD/AB. Problem (b)(ii): use the ASA condition for triangle equality. For problem (c), I recommend starting a new thread and explaining your difficulty.

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