Question
Find the error in each of the following solutions.
2𝑥^2 − 12𝑥 − 21 = 0
𝑥^2 − 6𝑥 =21/2
𝑥^2 − 6𝑥 + 9 =21/2− 9
(𝑥 − 3)^2 =3/2
𝑥 − 3 = ±√3/2
𝑥 − 3 = ±√3/√2
𝑥 = 3 ±√6/2
2𝑥^2 − 12𝑥 − 21 = 0
𝑥^2 − 6𝑥 =21/2
𝑥^2 − 6𝑥 + 9 =21/2− 9
(𝑥 − 3)^2 =3/2
𝑥 − 3 = ±√3/2
𝑥 − 3 = ±√3/√2
𝑥 = 3 ±√6/2
Answers
GPT 3.5
The error in each of the following solutions is as follows:
1) 𝑥^2 − 6𝑥 =21/2
The error is in the equation above. The correct equation should be 𝑥^2 − 6𝑥 + 9 = 21/2. This is because to complete the square, you need to add the square of half the coefficient of 𝑥 to both sides of the equation.
2) (𝑥 − 3)^2 =3/2
There is no error in this equation.
3) 𝑥 − 3 = ±√3/2
The error is in the calculation of the square root. The value should be ±√(3/2) instead of ±√3/2. This is because the square root should be applied to the entire fraction.
4) 𝑥 − 3 = ±√3/√2
The error is in the simplification of the square root. The value should be ±√(3/2) instead of ±√3/√2. This is because when dividing square roots, the square roots of the numerator and denominator should be taken separately.
5) 𝑥 = 3 ±√6/2
There is no error in this equation.
1) 𝑥^2 − 6𝑥 =21/2
The error is in the equation above. The correct equation should be 𝑥^2 − 6𝑥 + 9 = 21/2. This is because to complete the square, you need to add the square of half the coefficient of 𝑥 to both sides of the equation.
2) (𝑥 − 3)^2 =3/2
There is no error in this equation.
3) 𝑥 − 3 = ±√3/2
The error is in the calculation of the square root. The value should be ±√(3/2) instead of ±√3/2. This is because the square root should be applied to the entire fraction.
4) 𝑥 − 3 = ±√3/√2
The error is in the simplification of the square root. The value should be ±√(3/2) instead of ±√3/√2. This is because when dividing square roots, the square roots of the numerator and denominator should be taken separately.
5) 𝑥 = 3 ±√6/2
There is no error in this equation.