Solve for x in the radical equation sqrt(2x + 7) - x = 2.
Answer and explanation
Correct answer: C. x = 1
- Step 1: Isolate radical: sqrt(2x + 7) = x + 2. Step 2. Square both sides: 2x + 7 = x^2 + 4x + 4 => x^2 + 2x - 3 = 0 => (x + 3)(x - 1) = 0. Step 3. Check x = 1: sqrt(9) - 1 = 2 (valid). Check x = -3: sqrt(1) - (-3) = 4 != 2 (extraneous). Answer: x = 1 (discarding the extraneous solution x = -3). Why not the others: x = -3 is extraneous.
Practise more Algebra, Functions and Polynomials.
Free questions with an explanation for every one, and full timed University of the Philippines College Admission Test mock tests.
More Algebra, Functions and Polynomials questions
- What are all the real solutions to the quadratic equation 3x^2 - 11x + 6 = 0?
- If f(x) = (2x + 5) / (x - 3) for x != 3, what is the inverse function f^(-1)(x)?
- What is the remainder when the polynomial P(x) = 2x^4 - 3x^3 + x^2 - 5x + 7 is divided by x - 2?
- Solve for x in the logarithmic equation: log2(x - 2) + log2(x + 2) = 5.
- What is the solution set of the inequality |2x - 7| <= 5?
- Solve for x in the exponential equation 4^(x + 1) - 10 * 2^x - 24 = 0.