What Causes Discrepancies in Calculating Induced Charge Ratios?

[Mohammad Allahham]

Dear colleagues
I have this problem which I don't understand from where they got the solution I tried to solve it with slot of methods with the same answer which not the stated answer.
A point charge (q) is located a distance (b) from a grounded conducting sphere with radius (a) show that the ratio between the induced charge of the part in the front of (q) to the rest part is
√(a+b)/√(b-a)
I tried a lot of but each time I got the following answer
√(b² - a² +2ab)/√(b² - a² - 2ab)

 

[berkeman]

Dear colleagues
I have this problem which I don't understand from where they got the solution I tried to solve it with slot of methods with the same answer which not the stated answer.
A point charge (q) is located a distance (b) from a grounded conducting sphere with radius (a) show that the ratio between the induced charge of the part in the front of (q) to the rest part is
√(a+b)/√(b-a)
I tried a lot of but each time I got the following answer
√(b² - a² +2ab)/√(b² - a² - 2ab)

Welcome to the PF.

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Homework Statement

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The Attempt at a Solution

 

[haruspex]

each time I got the following answer

Looks like you are getting the wrong sign on the a² term, but as noted above, we can't guess how without seeing your working.
Note that your answer makes no sense as b tends to a. You might be able to make that test at various points in your working to see where it goes wrong.

I assume is b the distance from the surface (outside).