Question

√(2x-5)=1+√(x-3)

Answer 1

Answer:

x = 3 only

Step-by-step explanation:

$\sqrt{2x-5} =1+\sqrt{x-3}$

$\implies 2x-5=(1+\sqrt{x-3})^2\\\\ \implies 2x-5=x+2\sqrt{x-3} -2$

$\implies x-3=2\sqrt{x-3}$

$\implies (x-3)^2=(2\sqrt{x-3})^2$

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

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

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

$\implies x=3, x=7$

Check by substituting found values of x into original equation:

$x=3 \implies \sqrt{2(3)-5} =1+\sqrt{3-3} \implies 1 = 1 \ \ \ \checkmark$

$x=7 \implies \sqrt{2(7)-5} =1+\sqrt{7-3} \implies 3\neq 2 \ \ \ \ incorrect$