# Problem involving in surd

• Aug 11th 2012, 11:23 PM
alexander9408
Problem involving in surd
Find p,

√189 = √((p-1)^2+20) + √((p-4)^2+80)

Thanks.
• Aug 12th 2012, 12:39 AM
a tutor
Re: Problem involving in surd
Hint:

$\displaystyle \sqrt{189} = 3\sqrt{ 21}=\sqrt{21}+2\sqrt{21}=\sqrt{21}+\sqrt{84}$
• Aug 12th 2012, 12:40 AM
earboth
Re: Problem involving in surd
Quote:

Originally Posted by alexander9408
Find p,

√189 = √((p-1)^2+20) + √((p-4)^2+80)

Thanks.

The gen ral way to do such problems is: square --- islate the square-root --- square --- isolate the square-root ---

until you have a polynomial equation.

Square both sides:

$\displaystyle 189 = (p-1)^2+20 + 2\cdot \sqrt{(p-1)^2+20} \cdot \sqrt{(p-4)^2 + 80} + (p-4)^2 + 80$

Expand the brackets and isolate the square-root:

$\displaystyle 36-p^2+5p=\sqrt{(p-1)^2+20} \cdot \sqrt{(p-4)^2 + 80}$

Now square again, isolate, ....

and finally solve the equation. For confirmation only: You should come out with p = 2
• Aug 13th 2012, 09:18 AM
alexander9408
Re: Problem involving in surd
Thank you.