wearepink Posts: 2, Reputation: 1 New Member #1 Dec 25, 2005, 05:51 PM
squaring both sides twice
Here's a problem I am having troubles with.

_ ____
√x + √x – 5 = 5

Can someone help show me how to solve this?

Thanks,
B
 CaptainForest Posts: 3,645, Reputation: 393 Ultra Member #2 Dec 25, 2005, 11:37 PM
√x + √x – 5 = 5

Note that √x is also equal to x^1/2

Therefore,

√x + √x – 5 = 5
√x + √x = 5 + 5
2 √x = 10

√x = 10 / 2
√x = 5
x = 5^2/1
x = 25

Therefore, x=25

And a check,
√x + √x – 5 = 5
√25 + √25 – 5 = 5
5 + 5 - 5 = 5... Yes

Therefore, x=25
 wearepink Posts: 2, Reputation: 1 New Member #3 Dec 29, 2005, 07:06 AM
Squaring both sides twice - quadratic
Thanks for your help. When I posted my initial message it didn't post right. I am working on quadratic equations so I should wind up with x = ? Two times. The equation should be:

._.. . _____.
√x + √x – 5 = 5

Where the x - 5, not just the x, is under the square root symbol.

Thanks,
B
 reinsuranc Posts: 92, Reputation: 6 Junior Member #4 Jan 5, 2006, 12:17 AM
x^.5 + (x-5)^.5 = 5
It is easier to write such equations on this board as x^.5 + (x-5)^.5 = 5, instead of trying to draw square root symbols.

The answer to the above is 9:

x^.5 + (x-5)^.5 = 5

(x^.5 - 5)^2 = ( (x-5)^.5 )^2

x - 10x^.5 + 25 = x - 5

Let y = x^.5

y^2 - 10y + 25 = y^2 - 5

30 = 10y

y = 3

3 = x^.5

9 = x