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# AS Maths Help: Solving equations with roots/surds watch

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1. Hi there, i could do with a little bit of help here as i want to know the method of how to do these 2 questions:
Im sure this is quite simple in reality but i havent done these before so i would be grateful to know the method and the answer to these 2 questions please. Thanks.
"Solve the following equations"
1)

2)
2. Make a substitution and see what happens.
3. make substitution then solve.
first one t= 49
second one x= 16
4. Sorry but im still a bit unsure what to do. If someone could show the full working out even just for the first one, i will probably be able to do the second on my own. Thanks.
5. (Original post by ~Sparked~)
Sorry but im still a bit unsure what to do. If someone could show the full working out even just for the first one, i will probably be able to do the second on my own. Thanks.
I'll give you a different example.

Say you have . First notice that , so we can write this as

Making the substitution then turns this equation into

This is a quadratic equation, so you can factorise it using whatever method you like; and this will give:

...which has roots . This isn't the final answer though, because we need our roots to be in terms of ; but we know that , and so putting this back in, we get

or

The first of these would mean that , but beware of the second: when we write we implicitly use the positive root; and so there are no (real) numbers which have -2 as their principal square root, and so the only solution to the equation is .
6. Thanks, that clears things up.

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Updated: September 27, 2010
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