Express in the form

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- Jun 12th 2009, 07:53 PMmark1950[SOLVED] Expressing in the form?
Express in the form

- Jun 12th 2009, 08:40 PMSoroban
Hello, Mark!

Quote:

Express in the form

Square both sides: .

And we have: .

Equate coefficients: .

From

Multiply by

Factor: .

. . And the rational roots are: .

Substitute into

There are two solutions: .

- Jun 13th 2009, 03:08 AMmark1950
What's the difference between and ? Why do you have to inverse them to get ? Isn't it okay to just put ?

- Jun 13th 2009, 03:13 AMyeongil
No. Looking at this from Soroban's post:

See the in the denominator? The sign indicates that the number that follows has to be the opposite of whatever sign the number after the is. If the denominator is**+**6, then it simplifies to**-**2, and if the denominator is**-**6, it simplifies to**+**2.

The isn't used as often as . If you know trig, then you may have seen the sum/difference identity for cosine combined into one identity like this:

.

Of course, the two identities are these:

.

.

Note how the sign changes on the right side. That's the reason we use the sign.

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