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