I really need help with homework that is due tomorrow, and the problem is:

1. solve (√3x-5) - (√x+7) = 2

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- Sep 8th 2005, 05:46 PMu317dplease help urgent question
I really need help with homework that is due tomorrow, and the problem is:

1. solve (√3x-5) - (√x+7) = 2 - Sep 8th 2005, 06:37 PMMathGuruQuote:

Originally Posted by**u317d**

If so I would graph this equation on the left hand side and then graph y=2 and find where it intersects. - Sep 9th 2005, 11:03 AMticbol
solve (√3x-5) - (√x+7) = 2

If that is

sqrt(3x -5) -sqrt(x+7) = 2,

then,....

In cases like this, you have to isolate one radical to one side of the equation, then rationalize that isolated radical--and of course the other side of the equation too, at the same time--so that the radical sign will be eliminated. Then keep on isolating radicals and rationalizing them until you don't have anymore radicals left.

Here, the radicals are all square roots, so you just square a square root to rationalize it.

Too much talk, eh?

Let us do it.

sqrt(3x -5) -sqrt(x+7) = 2

Say, isolate the 1st radical,

sqrt(3x -5) = 2 +sqrt(x+7)

Square both sides,

(3x -5) = 2^2 +2*2*sqrt(x+7) +(x+7)

3x -5 = 4 +4sqrt(x+7) +x +7

We have one more radical left, so we isolate that again,

3x -5 -4 -x -7 = 4sqrt(x+7)

2x -16 = 4sqrt(x+7)

Divide both sides by 2,

x -8 = 2sqrt(x+7)

Square both sides,

x^2 -16x +64 = 4(x+7)

x^2 -16x +64 = 4x +28

x^2 -16x +64 -4x -28 = 0

x^2 -20x +36 = 0

(x -18)(x-2) = 0

x-18 = 0

x = 18 ---------***

x-2 = 0

x = 2 ------------***

Check if those satisfy the original "sqrt(3x -5) -sqrt(x+7) = 2"

When x=18,

sqrt(3*18 -5) -sqrt(18+7) =? 2

sqrt(49) -sqrt(25) =? 2

7 -5 =? 2

2 =? 2

Yes, so, OK.

When x=2

sqrt(3*2 -5) -sqrt(2+7) =? 2

sqrt(1) -sqrt(9) =? 2

1 -3 =? 2

-2 =? 2

No, so x=2 is not a solution.

Therefore, x = 18. -------answer. - Sep 9th 2005, 04:59 PMu317dthanks guys
Thanks guys, your help is greatly appreciated.