which is an extraneous solution to square root of 3x+1 = x-3

Question

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Answer 1

If √(3x+1)=x-3

then solution(s) must be x-3≥0,,,,x≥3

squaring both sides of given equation

3x-+1=x²-6x+9

setting left side to 0 and combining like terms

x²-9x+8=0

equation same as 0=(x-1)(x-8)

x=1 solution is extraneous.

Answer 2

sqr(3x+1) = x-3

square both sides,solve forx

3x+1 = x^2 -6x + 9

x^2 -9x +8

factor

(x-8)(x-1)=0

x=1 or 8

but plug them into the orginal equation

sqr4 =-2 isn't true as sqr only means the postive sqr

try 8

sqr25 = 8-3 = 5. That works

1 is the extraneous solution

whenever you multiply by a term with the variable, you introduce a potential extraneous solution. squaring both sides was multiplying by a term with the variable x