Question

For the given equations, classify the solutions as real rational and equal; real rational and not equal; real irrational and equal; or no real roots. Write your solution.

a) 1. Real rational and equal
b) 2. Real rational and equal
c) 3. Real rational and not equal
d) 4. Real rational and not equal
e) 5. Real irrational and equal
f) 6. No real roots

Answer 1

To classify the solutions of equations, it's essential to solve the equations, check for the type of roots, simplify the algebra, and ensure the reasonableness of the solution.

Step-by-step explanation:

The question asks for the classification of the solutions to given equations into different categories. The categories are: real rational and equal, real rational and not equal, real irrational and equal, or no real roots. To classify the solutions accurately, one needs to solve the equations and analyze the roots. This involves understanding how to perform operations with square roots, cube roots, and other algebraic manipulations, which may require use of a calculator. It is crucial to eliminate terms wherever possible to simplify the algebra and to examine the answer for reasonableness in terms of sense and units. The process includes writing down all given information, identifying necessary equations, and solving for the unknowns while ensuring the solution is logical and reasonable.