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

I. x2 – 23x + 90 = 0

II. y2 – 37y + 342 = 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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Best answer
Correct Answer - Option 3 : x ≤ y

Given:

I. x2 – 23x + 90 = 0

II. y2 – 37y + 342 = 0

Calculation:

I. x2 – 23x + 90 = 0

⇒ x2 - 18x - 5x + 90 = 0

⇒ x(x - 18) - 5(x - 18) = 0

⇒ (x - 18)(x - 5) = 0

⇒ x = 18, 5

II. y2 – 37y + 342 = 0

⇒ y2 - 18y - 19y + 342 = 0

⇒ y(y - 18) - 19(y - 18) = 0

⇒ (y - 18)(y - 19) = 0

⇒ y = 18, 19

Value of ‘x’

Relation

Value of ‘y’

18

=

18

18

19

5

18

5

19

 

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 comparison, all the values of x and y the relation is x y.

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