Question

If x be real and y =$\frac{x^{2} + 6x + 1}{2x}$, then which of the following is true:

• A. 2 < y < 4
• B. $\frac{5}{2}$< y <$\frac{7}{2}$
• C. Either y ≤ 2 or y ≥ 4
• D. None of these

Answer 1

Answer: (C)

Either y ≤ 2 or y ≥ 4

Answer 2

x² + x (6 –2y ) + 1 = 0

x is real so, D ≥ 0

36 + 4y² –24 y –4 ≥ 0

4y² –24y + 32 ≥ 0

y² –6y + 8 ≥ 0

⇒ y ≤ 2 of y ≥ 4

Hence choice (3) is correct.