Question 1085272
{{{sqrt(p+10) - sqrt(p-5) =sqrt(3+p)}}}.........square both sides


{{{(sqrt(p+10) - sqrt(p-5))^2 =(sqrt(3+p))^2}}}


{{{(sqrt(p+10))^2 -2sqrt(p+10) * sqrt(p-5)+ (sqrt(p-5))^2 =(sqrt(3+p))^2}}}


{{{p+10-2sqrt(p+10) * sqrt(p-5)+ p-5=3+p}}}


{{{2p+5-2sqrt((p - 5) (p + 10))=3+p}}}


{{{2p+5-3-p=2sqrt((p - 5) (p + 10))}}}


{{{p+2=2sqrt((p - 5) (p + 10))}}}.........square both sides


{{{(p+2)^2=(2sqrt((p - 5) (p + 10)))^2}}}


{{{p^2+4p+4=4 (p - 5) (p + 10)}}}


{{{p^2+4p+4= 4p^2 + 20 p - 200}}}


{{{ 4p^2 -p^2+ 20 p-4p - 200-4=0}}}


{{{ 3p^2+ 16p - 204=0}}}...factor

{{{(p - 6) (3 p + 34) = 0}}}

solutions:

{{{(p - 6) = 0}}}->{{{highlight(p=6)}}}

{{{(3 p + 34) = 0}}}->{{{p=-34/3}}}-> disregard negative solution if you given sqrt