Sqrt (p + 7) = sqrt (2p) + 1 #solve the radical equations, if possible.

Question

Sqrt (p + 7) = sqrt (2p) + 1 #solve the radical equations, if possible. 

Answer 1

√(p+7)=√(2p)+1

square both sides

p+7=2p+2√(2p)+1

p+7-2p-1=2√(2p)

-p+6=2√(2p)

square both sides again

P^2-12p+36=8p

p^2-12p+36-8p=0

p^2-20p+36=0

factor

(p-2)(p-18)=0

p-2=0

p=2

p-18=0

p=18

there is only one solution: p=2 (answer)

p=18 gives a false equation when you replace p by 18 in the original equation