Problem involving in surd

Please help me to solve this question.
Find p,

√189 = √((p-1)^2+20) + √((p-4)^2+80)

Please help, i don't know how to start off......
Thanks.

Re: Problem involving in surd

Hint:

$\sqrt{189} = 3\sqrt{ 21}=\sqrt{21}+2\sqrt{21}=\sqrt{21}+\sqrt{84}$

Re: Problem involving in surd

Quote:

Originally Posted by alexander9408

Please help me to solve this question.
Find p,

√189 = √((p-1)^2+20) + √((p-4)^2+80)

Please help, i don't know how to start off......
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.

With your problem:

Square both sides:

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

Expand the brackets and isolate the square-root:

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

Now square again, isolate, ....

and finally solve the equation. For confirmation only: You should come out with p = 2

Re: Problem involving in surd

Thank you.