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# How to do this

+1
15
7
+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
+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
+758
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Nice job. I tryed a dif method but it did not work :(

history  Jul 28, 2023
#6
+758
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Oh. I seem unintellegent. xD Oh well.

history  Jul 28, 2023
#3
+944
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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

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
+758
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I did not even notice that half of each sqrt is an perfect square.

history  Jul 28, 2023