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avatar+35 

Solve for y, \(\sqrt{50y}+2\sqrt{18y}=2\left(\sqrt{8y}+\sqrt{72y}\right)-5\)\(\)

I am trying to isolate the variable in one side and constant in other side, then I get

\(11\sqrt{2y}= 32y-5\),

after that I have no idea about how to solve the rest of the problem.

 Jul 27, 2023
 #1
avatar+1348 
-2

First, we can divide both sides by 11:

sqrt(2y) = 3y - 5/11

 

We can then square both sides of the equation to get rid of the radical:'

2y = 9y^2 - 35y + 25/121

This simplifies to 9y^2 - 44y + 25/121 = 0

 

Then we factor: (3y - 5/11)(3y - 5/22) = 0

So the solutions are y = 5/33 or y = 5/66.

 

But if we plug these in, we find that only y = 5/33 works.

 Jul 28, 2023
 #2
avatar+758 
0

Nice job. I tryed a dif method but it did not work :(

history  Jul 28, 2023
 #6
avatar+758 
0

Oh. I seem unintellegent. xD Oh well. 

history  Jul 28, 2023
 #3
avatar+944 
0

 

Solve for y.  sqrt(50y) + (2)sqrt(18y)  =  2(sqrt(8y) + sqrt(72y)) – 5   

 

First, I'm going to take all the perfect squares out from under the radicals.   

It looks like that's what you did, but I think there's a mistake in the addition.   

 

            (5)sqrt(2y) + (6)sqrt(2y)  =  (4)sqrt(2y) + (12)sqrt(2y) – 5   

 

                                (11)sqrt(2y)  =  (16)sqrt(2y) – 5    

 

                                  (5)sqrt(2y)  =  5     

 

                                       sqrt(2y)  =  5 / 5  =  1           

 

                                                2y  =  1       

 

                                                  y  =  1 / 2    

 

check answer   

 

                               sqrt(50y) + (2)sqrt(18y)  =  2(sqrt(8y) + sqrt(72y)) – 5    

 

                               sqrt(25)   + (2)sqrt(9)     =  2(sqrt(4)    + sqrt(36))    –5    

 

                                         5    +    6               =        4          +   12           – 5    

 

                                                                 11  =  11    

Looks pretty good.    

.

.

 Jul 28, 2023
 #7
avatar+758 
0

I did not even notice that half of each sqrt is an perfect square. 

history  Jul 28, 2023

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