Question

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

I. x2 - 35x + 124 = 0

II. y2 + 21y - 130 = 0

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

Answer 1

Correct Answer - Option 5 : x = y or relation between x and y can't be established.

Given:

I. x2 - 35x + 124 = 0

II. y2 + 21y - 130 = 0

Calculation:

From I,

x2 - 35x + 124 = 0

⇒ x2 - 31x - 4x + 124 = 0

⇒ x(x - 31) - 4(x - 31) = 0

⇒ (x - 31)(x - 4) = 0

Taking,

⇒ (x - 31) = 0 or (x - 4) = 0

⇒ x = 31 or 4

From II,

y2 + 21y - 130 = 0

⇒ y2 + 26y - 5y - 130 = 0

⇒ y(y + 26) - 5(y + 26) = 0

⇒ (y + 26)(y - 5) = 0

Taking,

⇒ (y + 26) = 0 or (y - 5) = 0

⇒ y = -26 or 5

Comparison between x and y (via Tabulation):

Value of x	Value of y	Relation
31	-26	x > y
31	5	x > y
4	-26	x > y
4	5	x < y

 

∴ x = y or relation between x and y can not be established.