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Allushta [10]
2 years ago
5

Eloise started to solve a radical equation in this way: Square root of negative 2x plus 1 − 3 = x Square root of negative 2x plu

s 1 − 3 + 3 = x + 3 Square root of negative 2x plus 1 = x + 3 Square root of negative 2x plus 1 − 1 = x + 3 − 1 Square root of negative 2 x = x + 2 (Square root of negative 2 x)2 = (x − 4)2 −2x = x2 − 8x + 16 −2x + 2x = x2 + 8x + 16 + 2x 0 = x2 + 10x + 16 0 = (x + 2)(x + 8) x + 2 = 0 x + 8 = 0 x + 2 − 2 = 0 − 2 x + 8 − 8 = 0 − 8 x = −2 x = −8 Both solutions are extraneous because they don't satisfy the original equation. What error did Eloise make?
Mathematics
2 answers:
sleet_krkn [62]2 years ago
6 0

Answer:

She subtracted 1 before squaring both sides.

(just took the quiz)


andreyandreev [35.5K]2 years ago
3 0
Here I copy the steps and indicate where the error is.

Square root of negative 2x plus 1 − 3 = x=> <span>this is the starting equation
</span>

√[ - 2x + 1] - 3 = x

Square root of negative 2x plus 1 − 3 + 3 = x + 3 in this step she added 3 to each side, which is fine

<span> Square root of negative 2x plus 1 = x + 3 <span>she made the addtions => fine</span></span>

Square root of negative 2x plus 1 − 1 = x + 3 – 1 due to <span>plus 1 in inside the square root, this step will not help</span>

<span> Square root of negative 2 x = x + 2 <span>wrong! she cannot simplify - 1 that is out of the square root with +1 that is inside the square root
</span></span>


<span>Then, from here on all is wrong, but she made other additional mistakes.</span>

(Square root of negative 2 x)2 = (x − 4)2 −2x <span> the right side should be (x+2)^2 which is x^2 + 4x +4 not (x-4)^2 - 2x</span>

Later she made a mistake changing the sign of -8x to +8x


Those are the mistakes. Finally, the global error is that she should verify whether the found values satisfied the original equation.

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