Question

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

I. 64x² + 24x – 70 = 0

II. 9y² – 27y + 20 = 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,

64x2 + 24x – 70 = 0

⇒ 64x2 – 56x + 80x – 70 = 0

⇒ 8x(8x – 7) + 10(8x – 7) = 0

⇒ (8x – 7)(8x + 10) = 0

Taking,

⇒ 8x – 7 = 0 or 8x + 10 = 0

⇒ x = 7/8 or x = -5/4

From II,

9y2 - 27y + 20 = 0

⇒ 9y2 – 12y – 15y + 20 = 0

⇒ 3y(3y – 4) – 5(3y – 4) = 0

⇒ (3y – 4)(3y – 5) = 0

Taking,

⇒ 3y – 4 = 0 or 3y – 5 = 0

⇒ y = 4/3 or y = 5/3

Comparison between x and y (via Tabulation):

x	y	Relation
7/8	4/3	x < y
-5/4	4/3	x < y
7/8	5/3	x < y
-5/4	5/3	x < y

 

∴ x < y