Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2013)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Algebra 2/Trigonometry Regents, January 2013

Part IV: A correct answer will receive 6 credits. Partial credit is possible.


39. Solve algebraically for x: SQRT

x² + x - 1 = 16x² - 24x + 9 + 11x = 7x + 3

Answer:

Get the radical by itself, and then square both sides of the eqaution. After that, solve the quadratic.

SQRT(x² + x - 1) + 11x = 7x + 3

SQRT(x² + x - 1) = -4x + 3

x² + x - 1 = (-4x + 3)²

x² + x - 1 = 16x² - 24x + 9

0 = 15x² - 25x + 10

0 = 3x² - 5x + 2

0 = 3x² - 3x - 2x + 2

0 = 3x(x - 1) - 2(x - 1)

0 = (3x - 2)(x - 1)

3x - 2 = 0 or x - 1 = 0

x = 2/3 or x = 1

Check the solutions:

SQRT((2/3)² + 2/3 - 1) + 11(2/3) ?= 7(2/3) + 3
23/3 = 23/3

SQRT((1)² + 1 - 1) + 11(1) ?= 7(1) + 3
12=/= 10, reject this solution

The solution is x = 2/3 only.

End of Exam.

More to come. Comments and questions welcome.

More Regents problems.

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