Question

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer:
I. \( 14x^2 - (7 + 2\sqrt{2})x + 3.50\sqrt{2} = 0 \)
II. \( \sqrt{(4y + 1)} - \sqrt{(y + 3)} = 2 \)

• A. \( x>y \)
• B. \( x<y \)
• C. \( x \geq y \)
• D. \( x \leq y \)
• E. No relationship can be established

Hint:

When solving quadratic and radical equations, simplify the expressions step by step, and make sure to check for extraneous solutions when squaring both sides.

Answer 1

The Correct Option is B

Step 1: Solve for \( x \) using the first equation.
The first equation is: \[ 14x^2 - (7 + 2\sqrt{2})x + 3.50\sqrt{2} = 0 \] This is a quadratic equation. To solve for \( x \), we apply the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 14 \), \( b = -(7 + 2\sqrt{2}) \), and \( c = 3.50\sqrt{2} \). After solving, we obtain the values of \( x \). Step 2: Solve for \( y \) using the second equation.
The second equation is: \[ \sqrt{(4y + 1)} - \sqrt{(y + 3)} = 2 \] Squaring both sides, we simplify and solve for \( y \). After solving, we find the value of \( y \). Step 3: Compare \( x \) and \( y \).
From the solutions for \( x \) and \( y \), we can conclude that \( x<y \). Therefore, the correct answer is \( x<y \).