Question

Two equations I and II are given below in question. You have to solve these equations and give the answer.

I. x2 – 16x + 63 = 0

II. y2 - 13y + 42 = 0

1. x < y
2. x > y
3. x ≤ y
4. x ≥ y
5. x = y or the relation between x and y can't be established.

Answer 1

Correct Answer - Option 4 : x ≥ y

Given:

I. x² – 16x + 63 = 0

II. y² - 13y + 42 = 0

Calculation:

I. x² – 16x + 63 = 0

⇒ x² – 7x – 9x + 63 = 0

⇒ x(x – 7) – 9(x – 7) = 0

⇒ (x – 7)(x – 9) = 0

⇒ x = 7, 9

II. y² - 13y + 42 = 0

⇒ y² – 6y – 7y + 42 = 0

⇒ y(y – 6) – 7(y – 6) = 0

⇒ (y – 6)(y – 7) = 0

⇒ y = 6, 7

Value of ‘x’	Relation	Value of ‘y’
7	>	6
7	=	7
9	>	6
9	>	7

When we compared the values of ‘x’ and ‘y’ in the table above, we found that there are TWO relations between X and Y i.e. > and =. So, a relation between x and y is “x ≥ y”.

∴ After comparing all the values of x and y, the relation between x and y is “x ≥ y”.