Question

In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.

I. x² – 29x + 54 = 0

II. y² + 28y – 60 = 0

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

Answer 1

Correct Answer - Option 4 : x ≥ y

Calculation:

I. x² – 29x + 54 = 0

⇒ x² – 27x – 2x + 54 = 0

⇒ x(x – 27) – 2(x – 27)= 0

⇒ (x – 27)(x – 2) = 0

⇒ x = 27, 2

II. y² + 28y – 60 = 0

⇒ y² + 30y – 2y – 60 = 0

⇒ y(y + 30) – 2(y – 30) =0

⇒ (y + 30)(y – 2) = 0

⇒ y = (-30), 2

Comparison between x and y (via Tabulation):

Value of ‘x’	Relation	Value of ‘y’
27	>	-30
27	>	2
2	>	-30
2	=	2

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

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