Find the error in each of the following solutions. Explain your reasoning
2š„^2 ā 12š„ ā 21 = 0
š„^2 ā 6š„ =21/2
š„^2 ā 6š„ + 9 =21/2ā 9
(š„ ā 3)^2 =3/2
š„ ā 3 = Ā±ā3/2
š„ ā 3 = Ā±ā3/ā2
š„ = 3 Ā±ā6/2
The error in each of the following solutions is the incorrect simplification of the equations or expressions.
1. The error is in simplifying š„^2 ā 6š„ as 21/2. This is incorrect because 21/2 is not the simplified form of š„^2 ā 6š„. The correct simplification is š„^2 ā 6š„ - 21 = 0.
2. The error is in subtracting 9 from 21/2 without simplifying the right side of the equation. The correct simplification should be š„^2 ā 6š„ + 9 = 21/2 - 9/1.
3. The error is in not simplifying the right side of the equation. The correct equation should be (š„ ā 3)^2 = (3/2) * (2/2).
4. The error is in taking the square root of 3/2 without dividing the square root of 3 and 2. The correct equation should be š„ ā 3 = Ā±ā(3/2).
5. The error is in incorrectly dividing the square root of 3 by the square root of 2. The correct equation should be š„ ā 3 = Ā±ā(3/ā2).
6. The error is in not simplifying the expression correctly. The correct equation should be š„ = 3 Ā± (ā6/2).