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.

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- Aug 11th 2012, 11:23 PMalexander9408Problem 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. - Aug 12th 2012, 12:39 AMa tutorRe: 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 AMearbothRe: Problem involving in surd
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:

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

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 AMalexander9408Re: Problem involving in surd
Thank you.