215k views
9 votes
√(2x-5)=1+√(x-3)

btw the solution is not x=7, 3 i tried that already. Also pls show steps i will give u 5 stars and a heart.

User Belogix
by
7.0k points

1 Answer

5 votes

Answer:

x = 3 only

Explanation:


√(2x-5) =1+√(x-3)


\implies 2x-5=(1+√(x-3))^2\\\\ \implies 2x-5=x+2√(x-3) -2


\implies x-3=2√(x-3)


\implies (x-3)^2=(2√(x-3))^2


\implies x^2-6x+9=4x-12


\implies x^2-10x+21=0


\implies (x-3)(x-7)=0


\implies x=3, x=7

Check by substituting found values of x into original equation:


x=3 \implies √(2(3)-5) =1+√(3-3) \implies 1 = 1 \ \ \ \checkmark


x=7 \implies √(2(7)-5) =1+√(7-3) \implies 3\\eq 2 \ \ \ \ incorrect

User Matt Dressel
by
7.3k points