could someone show me how to solve radical problems?

RedheadSTL

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Thanks in advance!

1) 2 SQRT (x + 1) = 6

2) SQRT(3x^2 - 9) = 2x

3) [sqrt(x) + 1] / [sqrt(x) – 1] + [sqrt(x) – 1] / [sqrt(x) + 1]
 

stapel

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1) Divide through by 2, square both sides, and solve the linear equation.

2) Square both sides. Then solve the resulting quadratic equation.

3) If this is an equation, there's a typo, because there is no "equals" sign. If this is an expression, then follow the procedure they taught you for rationalizing denominators (which will, as a side effect in this case, give you the common denominator).

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.
 

RedheadSTL

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Thanks.

So I divide everything by 2. (x+1)/2 = 3

Is that correct so far?
 

stapel

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RedheadSTL said:
So I divide everything by 2. (x+1)/2 = 3

Is that correct so far?
Two divided by two is 1, not 1/2. And what happened to the square root?

Eliz.
 

Denis

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RedheadSTL said:
3) [sqrt(x) + 1] / [sqrt(x) – 1] + [sqrt(x) – 1] / [sqrt(x) + 1]
hint: a/b + b/a = (a^2 + b^2) / (ab)
 
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