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

I. x2 - 27x + 180 = 0

II. y2 – 13y + 12 = 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.

1 Answer

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Correct Answer - Option 4 : x ≥ y

Given:

I. x2 - 27x + 180 = 0

II. y2 – 13y + 12 = 0

Calculation:

I. x2 - 27x + 180 = 0

⇒ x– 15x – 12x + 180 = 0

⇒ x(x – 15) - 12(x – 15)= 0

⇒ (x – 15)(x – 12) = 0

⇒ x = 15, 12

II. y2 – 13y + 12 = 0

⇒ y– 12y – y + 12 = 0

⇒ y(y – 12) – (y – 12) =0

⇒ (y – 12)(y – 1) = 0

⇒ y = 12, 1

Value of ‘x’

Relation

Value of ‘y’

15

12

15

1

12

=

12

12

1


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.

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