Show work and solve for √ ( 5 x − 9 ) − 1 = x.
2 answers:
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
<u>Answer:</u>
x = -2 and x = 5
<u>Step-by-step explanation:</u>

Taking square on both sides of the equation to get:

Factorizing this equation to get:

Checking for any extraneous solution:
Put x=-2 in the given expression:
---> extraneous solution
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