JEE Advanced Maths: Basic Algebra (Equations) questions with solutions

Q1. Solve the equation sqrt(2x + 1) = sqrt(x) + 1 for x.

1. x = 0 or x = 4
2. x = 4 only
3. x = 1 only
4. no real solution

Answer: x = 0 or x = 4

Square: 2x + 1 = x + 2sqrt(x) + 1 ⇒ x = 2sqrt(x) ⇒ x - 2sqrt(x) = 0 ⇒ sqrt(x)(sqrt(x) - 2) = 0 ⇒ sqrt(x) = 0 or 2 ⇒ x = 0 or x = 4. Both satisfy the original (x=0: sqrt(1)=1=0+1 ✓; x=4: sqrt(9)=3=2+1 ✓).

Q2. Solve |2x - 3| + 4 = 2 for real x.

1. no solution
2. x = 3/2
3. x = 1/2 or x = 5/2
4. x = -1/2

Answer: no solution

Isolating gives |2x - 3| = -2. Since an absolute value is always >= 0, it can never equal -2. Therefore there is no real solution.