SOLUTION: Hi I need help with these radical equation questions. Thanks in advance :) Solve each equation and check for extraneous solutions: 1. [sqrt(2x^2 - 1)]=x A.[sqrt(1/3)]

Algebra ->  Statistics  -> Displaying-distributions -> SOLUTION: Hi I need help with these radical equation questions. Thanks in advance :) Solve each equation and check for extraneous solutions: 1. [sqrt(2x^2 - 1)]=x A.[sqrt(1/3)]       Log On


   

Question 950712: Hi I need help with these radical equation questions. Thanks in advance :)
Solve each equation and check for extraneous solutions:
1. [sqrt(2x^2 - 1)]=x
A.[sqrt(1/3)]
B.{-1,1}
C.{-1/2,1}
D.1
E.0
F.none of the above
2.[sqrt(2x^2 + 5x + 6)]=x
A.no solution
B.{-2,-3}
C.{2,3}
D.-2
E.3
F.0
3. [sqrt(x + 3)] = 2[SQRT(x)]
A.no real solution
B.3
C.{-3,3}
D.0
E.3/2
F.1
4.[sqrt(2x^2 + x - 12)] = x
A.[sqrt(6)]
B.3
C.no solution
D.[sqrt(12)]
E.2
F.{-2,2}
5.[sqrt(2x^2 + 6x + 4)] = x + 1
A.1
B.{-3, -1}
C.{-3/2, -1}
D.no solution
E.-1
F.-3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.
%28sqrt%282x%5E2+-1%29%29=x.......square both sides
%28%28sqrt%282x%5E2+-1%29%29%29%5E2=x%5E2
2x%5E2-1=x%5E2
2x%5E2-x%5E2-1=0
x%5E2-1=0
%28x-1%29%28x%2B1%29=0
solutions:
%28x-1%29=0=>x=1
%28x%2B1%29=0=>x=-1
answer is:
B.{-1,1}



2.
sqrt%282x%5E2+%2B+5x+%2B+6%29=x
%28sqrt%282x%5E2+%2B+5x+%2B+6%29%29%5E2=x%5E2
2x%5E2+%2B+5x+%2B+6=x%5E2
2x%5E2-x%5E2+%2B+5x+%2B+6=0
x%5E2+%2B+5x+%2B+6=0
x%5E2%2B+2x%2B+3x+%2B+6=0
%28x%5E2%2B+2x%29%2B+%283x+%2B+6%29=0
x%28x%2B+2%29%2B+3%28x+%2B+2%29=0
%28x%2B+3%29%28x+%2B+2%29=0
solutions:
%28x%2B+3%29=0=>x=-3
%28x+%2B+2%29=0=>x=-2
answer:
B.{-2,-3}


3.
sqrt%28x+%2B+3%29+=+2sqrt%28x%29
%28sqrt%28x+%2B+3%29%29%5E2+=%28+2sqrt%28x%29%29%5E2
x+%2B+3+=+4x
3+=+4x-x
3+=+3x
x=1
answer:
F.1
since x=1, sqrt%281+%2B+3%29+=+2sqrt%281%29=>sqrt%284%29+=+2%2A1=>2+=+2
so, these lines intersect at (1,2)



4.
sqrt%282x%5E2+%2B+x+-12%29+=+x
%28sqrt%282x%5E2+%2B+x+-12%29%29%5E2+=+x%5E2
2x%5E2+%2B+x+-12+=+x%5E2
2x%5E2+-x%5E2%2B+x+-12+=+0
x%5E2%2B+x+-12+=+0
x%5E2%2B+4x-3x+-12+=+0
%28x%5E2%2B+4x%29-%283x+%2B12%29+=+0
x%28x%2B+4%29-3%28x+%2B4%29+=+0
%28x%2B4%29%28x-3%29=0
solutions:
%28x%2B4%29=0=>x=-4
%28x-3%29=0=>x=3
answer is:
B.3

5.
sqrt%282x%5E2+%2B+6x+%2B+4%29+=+x+%2B+1
%28sqrt%282x%5E2+%2B+6x+%2B+4%29%29%5E2+=+%28x+%2B+1%29%5E2
2x%5E2+%2B+6x+%2B+4=+x%5E2%2B2x+%2B+1
2x%5E2+%2B+6x+%2B+4-x%5E2-2x+-+1=0
x%5E2+%2B+4x+%2B+3=0
x%5E2+%2Bx%2B+3x+%2B+3=0
%28x%5E2+%2Bx%29%2B+%283x+%2B+3%29=0
x%28x+%2B1%29%2B+3%28x+%2B+1%29=0
%28x+%2B3%29%28x+%2B+1%29=0

solutions:
%28x+%2B3%29=0=>x=-3
%28x+%2B+1%29=0=>x=-1
answer:
B.{-3, -1}