Multiple choice

In the following questions two equations I and II are given. You have to solve both the equations and give answer. $( (I) \ (x + 1)^{2} + 1 = 2(x +3) )$ $( (II) \ (2y – 1) (y – 3) = (y – 5) (y – 1) )$

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or the relationship cannot be determined.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Equation I: (x+1)²+1 = 2(x+3) gives x²+2x+1+1 = 2x+6, so x²-4=0, x = ±2. Equation II: (2y-1)(y-3) = (y-5)(y-1) gives 2y²-7y+3 = y²-6y+5, so y²-y-2=0, (y-2)(y+1)=0, y = 2 or y = -1. When x=2, x=y; when x=-2, x < y=-1. The relationship varies, so option E is correct. Option B (x ≥ y) is wrong because x=-2 is less than y=-1.

Keep practicing — related questions