Stuck on a algebraic fraction question.

[Kris_study]

I have passed this quiz and need to move on with my life, but I can't let go of this question.
I have google calculated it but I just don't see how to get the answer!
Does anyone get this one easily? Can you explain it?

 

[Deleted member 4993]

I have passed this quiz and need to move on with my life, but I can't let go ofView attachment 23140 this question.
I have google calculated it but I just don't see how to get the answer!
Does anyone get this one easily? Can you explain it?

For us to check your work - you need to share your work. How did you try to solve the problem?

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

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

Please share your work/thoughts about this problem.

 

[pka]

I have passed this quiz and need to move on with my life, but I can't let go of this question.

To Kris_study, Do you know the correct answer or not?
If not then show us what you have tried.
If you do know, then tell us what confuses you.

 

[Dr.Peterson]

I have passed this quiz and need to move on with my life, but I can't let go ofView attachment 23140 this question.
I have google calculated it but I just don't see how to get the answer!
Does anyone get this one easily? Can you explain it?

Did you apply the Pythagorean theorem?

Do you know how to square a binomial? And to recognize the square of a binomial?

Those are the most important steps. You may have made a mistake in the squaring, or in signs.

 

[Kris_study]

Hello. Thank you for replying.

No, I don't know which one is the correct answer.

I tried this:

c^2 = (a^2-b^2)^2 + (2ab)^2

a = (2ab)^2 = 4a^2b^2

b = (a^2-b^2)(a^2-b^2) = a^4 -(a^2 b^2) -(b^2 a^2) +b^4

b = a^4 -2(a^2b^2) + b^4

c^2 = a^4 - 2a^2b^2 + b^4 + 4a^2b^2

c = /a^4 + b^4 + 2a^2b^2

Which doesn't match any of the options. So I guessed 1 and was wrong.
I am not really sure how to tackle this question.

 

[Deleted member 4993]

Hello. Thank you for replying.

No, I don't know which one is the correct answer.

I tried this:

c^2 = (a^2-b^2)^2 + (2ab)^2

a = (2ab)^2 = 4a^2b^2

b = (a^2-b^2)(a^2-b^2) = a^4 -(a^2 b^2) -(b^2 a^2) +b^4

b = a^4 -2(a^2b^2) + b^4

c^2 = a^4 - 2a^2b^2 + b^4 + 4a^2b^2

c = /a^4 + b^4 + 2a^2b^2

Which doesn't match any of the options. So I guessed 1 and was wrong.
I am not really sure how to tackle this question.

Use
a^4 + b^4 + 2a^2b^2 = (a^2 + b^2)^2

 

[Steven G]

Hello. Thank you for replying.

No, I don't know which one is the correct answer.

I tried this:

c^2 = (a^2-b^2)^2 + (2ab)^2

a = (2ab)^2 = 4a^2b^2

b = (a^2-b^2)(a^2-b^2) = a^4 -(a^2 b^2) -(b^2 a^2) +b^4

b = a^4 -2(a^2b^2) + b^4

c^2 = a^4 - 2a^2b^2 + b^4 + 4a^2b^2

c = /a^4 + b^4 + 2a^2b^2

Which doesn't match any of the options. So I guessed 1 and was wrong.
I am not really sure how to tackle this question.

You want to find c so why are you solving for a and b?
You have what c^2 equals. Just clean up the other side and then take the square root of both sides.

c^2 = (a^2-b^2)^2 + (2ab)^2 so c = sqrt ((a^2-b^2)^2 + (2ab)^2). Now which is the choice that this matches with?

 

[Kris_study]

Use
a^4 + b^4 + 2a^2b^2 = (a^2 + b^2)^2

Ahh, I can see it now. I couldn't stop wondering what I was missing here, I think I even wrote that down at one point and thought no, that wouldn't be it. But there it is. Thank you for that