Correct Answer - Option 5 : x = y or the relationship between x and y cannot be established.
I. x2 – 14x + 33 = 0
⇒ x2 – 11x – 3x + 33 = 0
⇒ x(x – 11) – 3(x – 11) = 0
⇒ (x – 11)(x – 3) = 0
Then, x = 11 or x = 3
Now,
II. y2 – 20y + 99 = 0
⇒ y2 – 11y – 9y + 99 = 0
⇒ y(y – 11) – 9(y – 11) = 0
⇒ (y – 11)(y – 9) = 0
Then, y = 11 or y = 9
Now,
Comparison between x and y (via Tabulation):
Value of x |
Value of y |
Relation |
3 |
9 |
x < y |
3 |
11 |
x < y |
11 |
9 |
x > y |
11 |
11 |
x = y |
∴ We can clearly see that the relationship cannot be established