Solve radical eqn: (root 2x-1) - (root x+11) = -1

[sfin]

Solve (root 2x-1) - (root x+11) = -1.

(root 2x-1) - (root x+11) = -1
(root 2x-1) = (root x+11) - 1
2x-1 = ((root x+11) - 1)^2
2x-1 = x+11 - 2(root x+11) + 2
2(root x+11) = 14 - x
4(x+11) = 196 - 28x + x^2
4x + 44 = 196 - 28x + x^2
x^2 - 32x + 152 = 0
And now I cannot factor this. When I use the quadratic equation, I get wrong answers also. The answer is 5. Could someone please show me how to get this answer?

Thanks,
sf

 

[axrw]

I think you just made a small error in your math.

sqrt(2x - 1) - sqrt(x + 11) = -1

sqrt (2x - 1) = sqrt(x + 11) - 1

squaring both sides

2x - 1 = x + 11 - 2[sqrt(x + 11)] + 1

x - 13 = -2[sqrt(x + 11)]

(x - 13)/-2 = sqrt(x + 11)

squaring both sides again

(x^2 - 26x + 169)/ 4 = x + 11

multiply both sides by 4 to get rid of fraction

x^2 - 26x + 169 = 4x + 44

x^2 - 30x + 125 = 0

(x - 5)(x - 25) = 0

and only x = 5 seems to work in the original equation.

 

[Denis]

sqrt(2x - 1) - sqrt(x + 11) = -1

Easier to square if you rearrange:

sqrt(2x - 1) + 1 = sqrt(x + 11) ; now square:

2x - 1 + 2sqrt(2x - 1) + 1 = x + 11

2sqrt(2x - 1) = -x + 11 ; square again:

4(2x - 1) = x^2 - 22x + 121

8x - 4 = x^2 - 22x + 121

x^2 - 30x + 125 = 0 : as per axrw

 

[sfin]

thanks, way too late here ....

 

[stapel]

thanks, way too late here ....

If two replies within seventy minutes is "way too late", then you might want to consider contracting with a paid service.

(As was mentioned in the "Read Before Posting!!" thread you read, poster to free services such as this should expect to wait hours, if not days, for replies from the volunteers. Instant on-demand guaranteed replies generally require rather larger pre-paid fees.)

My best wishes to you.

Eliz.

 

[sfin]

OOps!

Didn't mean it like that, Eliz!

It was way too late at night for me to be doing math! The response times I got were great, considering it was past midnight for me.

Sorry for the confusion,
sfin