Radical equations and inequalities

9000024805

Level: 
C
A falling body dropped at a velocity 60ms−1. Find the initial height h, if the relation between the velocity and the initial height h is v=2hg. Use g=10ms−2 for acceleration of gravity.
The initial height is between 150m and 200m.
The initial height is smaller than 100m.
The initial height is between 100m and 150m.
The initial height is bigger than 200m.

9000024802

Level: 
A
Consider the equation x2−2x+1=x+2 and the equation which arises from this equation by squaring both sides of the equation, i.e. the equation (x2−2x+1)2=(x+2)2. Identify a true statement.
Both equations are equivalent only if x≥−2.
Both equations are equivalent.
Both equations are equivalent only if x≤−2.
None of the above.

9000024803

Level: 
A
Removing radical in an equation by squaring both sides may enrich the set of solutions of this equation and checking the solutions of the new equation in the original equation may be necessary. Identify a correct conclusion in the particular case of the following equation. −x2−2x+1=x
If we look for the solution in the set R−, then squaring both sides of the equation gives an equivalent equation. The checking of the solution is not necessary.
If we look for the solution in the set R+, then squaring both sides of the equation gives an equivalent equation. The checking of the solution is not necessary.
If we look for the solution in the set R, then squaring both sides of the equation gives an equivalent equation. The checking of the solution is not necessary.
None of the above.