If 3+(sqrt(5)) = a, 1/3-(sqrt(5))=?

[ksardas21]

 

[Deleted member 4993]

View attachment 26134

Use:

\(\displaystyle \frac{1}{3-\sqrt{5}} \ = \frac{3 \ \ + \ \sqrt{5}}{(3\ - \ \sqrt{5}) \ * \ (3 \ + \ \sqrt{5})}\)​

​

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

If 3+(sqrt(5)) = a, 1/3-(sqrt(5))=?
View attachment 26134

What you mean to ask is, If 3+sqrt(5) = a, 1/(3-sqrt(5))=?

Try rationalizing the denominator (using the conjugate).

 

[ksardas21]

What you mean to ask is, If 3+sqrt(5) = a, 1/(3-sqrt(5))=?

Try rationalizing the denominator (using the conjugate).

I attached the photo, I don't know how to write square root here

 

[Deleted member 4993]

I attached the photo, I don't know how to write square root here
View attachment 26140

You were told to Use:

\(\displaystyle \displaystyle \frac{1}{3-\sqrt{5}} \ = \frac{3 \ \ + \ \sqrt{5}}{(3\ - \ \sqrt{5}) \ * \ (3 \ + \ \sqrt{5})}\)

Can you simplify the denominator (of the Right-hand-side of the equation above?

 

[Dr.Peterson]

I attached the photo, I don't know how to write square root here
View attachment 26140

You wrote sqrt just right. What you omitted were the necessary parentheses to make it mean what you show in the image. I was trying to help you learn how to communicate clearly.

Now do what I said.

 

[ksardas21]

You were told to Use:

\(\displaystyle \displaystyle \frac{1}{3-\sqrt{5}} \ = \frac{3 \ \ + \ \sqrt{5}}{(3\ - \ \sqrt{5}) \ * \ (3 \ + \ \sqrt{5})}\)

Can you simplify the denominator (of the Right-hand-side of the equation above?

Yes! got it
the answer is