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.

x²-21x+108=0

y²-14y+48=0

The correct option is If x>y.

Step 1: Solve Equation I for x

$x^2-21x+108=0$

We split the middle term to factorize the equation. We find two factors of 108 whose sum is -21, which are -9 and -12:

$x^2-9x-12x+108=0$

$x(x-9)-12(x-9)=0$

$(x-9)(x-12)=0$

Thus, the roots for x are:

$x=9$ or $x=12$

Step 2: Solve Equation II for y

$y^2-14y+48=0$

We find two factors of 48 whose sum is -14, which are -6 and -8:

$y^2-6y-8y+48=0$

$y(y-6)-8(y-6)=0$

$(y-6)(\mathrm{y<mo>-</mo><mn>8</mn><mo>)</mo><mo>=</mo><mn>0</mn>}$

Thus, the roots for y are:

$y=6$ or $y=8$

Step 3: Compare the values of x and y

Comparing each value of x with every value of y:
- For $x=9$: $9>6$ and $9>8$
- For $x=12$: $12>6$ and $12>8$

In all cases, every root of x is strictly greater than every root of y.

Hence, the relation between x and y is x > y.