Question

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

I. 13x² - 58x + 64 = 0

II. 12y² + 46y + 44 = 0

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

Answer 1

Correct Answer - Option 2 : x > y

Calculations:

From I,

13x2 - 58x + 64 = 0

⇒ 13x2 – 26x – 32x + 64 = 0

⇒ 13x(x – 2) – 32(x – 2) = 0

⇒ (x – 2)(13x – 32) = 0

Taking,

⇒ x – 2 = 0 or 13x – 32 = 0

⇒ x = 2 or x = 32/13

From II,

12y2 + 46y + 44 = 0

⇒ 12y2 + 24y + 22y + 44 = 0

⇒ 12y(y + 2) + 22(y + 2) = 0

⇒ (y + 2)(12y + 22) = 0

Taking,

⇒ y + 2 = 0 or 12y + 22 = 0

⇒ y = – 2 or y = – 11/6

Comparison between x and y (via Tabulation):

x	y	Relation
2	- 2	x > y
32/13	- 2	x > y
2	- 11/6	x > y
32/13	- 11/6	x > y

 

∴ x > y