Question

√(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.

Answer 1

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`