Mathematics, 01.12.2021 07:20 meganwintergirl
Eloise started to solve a radical equation in this way:
square root of negative 2x plus 1 β 3 = x
square root of negative 2x plus 1 β 3 + 3 = x + 3
square root of negative 2x plus 1 = x + 3
square root of negative 2x plus 1 β 1 = x + 3 β 1
square root of negative 2 x = x + 2
(square root of negative 2 x)2 = (x β 4)2
β2x = x2 β 8x + 16
β2x + 2x = x2 + 8x + 16 + 2x
0 = x2 + 10x + 16
0 = (x + 2)(x + 8)
x + 2 = 0 x + 8 = 0
x + 2 β 2 = 0 β 2 x + 8 β 8 = 0 β 8
x = β2 x = β8
Both solutions are extraneous because they don't satisfy the original equation.
What error did Eloise make?
A) She added 2x after squaring both sides.
B) She subtracted 1 before squaring both sides.
C) She factored x2 + 10x + 16 incorrectly.
D) She did not check for extraneous solutions.
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Eloise started to solve a radical equation in this way:
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