sqrt (5x - 9) - 1 = x
sqrt(5x - 9) = x + 1
Square both sides:_
5x - 9 = x^2 + 2x + 1
x^2 - 3x + 10 = 0
(x - 5)(x + 2) = 0
x = 5 or -2.
Lets look for for any extraneous solutions:-
x = 5 ; sqrt (5*5-9) - 1 = sqrt16 - 1 = 3 and x = 3 (right hand side of equation)
so x = 5 is a solution
x = -2: sqrt(5*-2 - 9) - 1 = sqrt (-19) - 1 and x = -2 so this is extraneous
Answer:- One solution x = 5
Answer:
x = -2 and x = 5
Step-by-step explanation:
[tex]\sqrt{(5x-9)} -1=x\\\\\sqrt{(5x-9)}=x+1[/tex]
Taking square on both sides of the equation to get:
[tex](\sqrt{5x-9})^2=(x+1)^2\\\\5x-9=x^2+2x+1\\\\x^2+2x-5x+1+9=0\\\\x^2-3x+10=0[/tex]
Factorizing this equation to get:
[tex]x^2+2x-5x+10=0\\\\x(x+2)-5(x+2)=0\\\\(x+2)(x-5)=0\\\\x=-2, x=5[/tex]
Checking for any extraneous solution:
Put x=-2 in the given expression:
[tex]\sqrt{5(-2)-9} -1=-2\\\\\sqrt{-19}-1 \neq -2[/tex] ---> extraneous solution
