Directions (42-46) : In each question two equations numbered (I) and (II) are given. You have to solve both the equations and mark appropriate answer.

x³=729

y²-15y+54=0

Correct Answer: If x>=y

Step 1: Solve Equation (I) for x

The first equation is given as:

$x^3=729$

Taking the cube root on both sides:

$x=\sqrt[3]{729}$

$x=9$

Step 2: Solve Equation (II) for y

The second equation is a quadratic equation:

$y^2-15y+54=0$

We need to find two numbers that multiply to 54 and add up to -15. These numbers are -9 and -6.

Splitting the middle term:

$y^2-9y-6y+54=0$

$y(y-9)-6(y-9)=0$

$(y-9)(y-6)=0$

Therefore, the roots for $y$ are:

$y=9$ or $y=6$

Step 3: Compare the values of x and y

- When $y=9$, $x=9$, so $x=y$.

- When $y=6$, $x=9$, so $x>y$.

Combining both cases, we get $x\ge y$.