Solving for y

[learningmathagain]

When x=2 and y=3, (xy+3)^1/4((x+y)^1/2−(y−1)x⁻¹) = ?

The answers are given as multiple choice and I can't seem to get the right one. Here's my expanded equation:

(2*3+3)^1/4((2+3)^1/2 - (2-1)(3^-1) = ?

9^1/4 (5^1/2 - 2/2) = ?

9^1/4 (5^1/2 - 1) = ?

9^1/4 (5^1/2) - 9^1/4 = ?

And here's where I get stuck. I'm not sure how to simplify this more, but apparently the answer is 15^1/2 - 3^1/2 but I'm not sure how that is. Would be happy for some help!

 

[R.M.]

9^1/4 = (9^1/2)^1/2 = (3^2x1/2)^1/2 = 3^1/2
See what you can do with this.

 

[pka]

You should give all the choices so that we can see what is going on.
I see one mistake in the first line:
if \(x=2~\&~y=3\) then \((y-1)x^{-1}=(2)(2)^{-1}=1\)

 

[Steven G]

(2-1)(3^-1)
Although that 3 should be a 2 I am still interested in how you got 2/2. Please show those steps.

 

[Steven G]

9^1/4 = (9^1/2)^1/2 = ....

 

[Deleted member 4993]

When x=2 and y=3, (xy+3)^1/4((x+y)^1/2−(y−1)x⁻¹) = ?

The answers are given as multiple choice and I can't seem to get the right one. Here's my expanded equation:

(2*3+3)^1/4((2+3)^1/2 - (2-1)(3^-1) = ?

9^1/4 (5^1/2 - 2/2) = ?

9^1/4 (5^1/2 - 1) = ?

9^1/4 (5^1/2) - 9^1/4 = ?

And here's where I get stuck. I'm not sure how to simplify this more, but apparently the answer is 15^1/2 - 3^1/2 but I'm not sure how that is. Would be happy for some help!

(2*3+3)^1/4((2+3)^1/2 - (3-1)(2^-1) = ?

9^1/4 (5^1/2 - 2/2) = ?

9^1/4 (5^1/2 - 1) = ?

9^1/4 (5^1/2) - 9^1/4 = ? ..................... You are almost there...

3^1/2 (5^1/2) - 3^1/2

= (3*5)^1/2 - 3^1/2 .......continue.....

 

[learningmathagain]

9^1/4 = (9^1/2)^1/2 = (3^2x1/2)^1/2 = 3^1/2
See what you can do with this.

Thank you! That made everything more clear, I didn't think to simplify this further.