Direction (1-5): In each question twp equations are provided, On the basis of these have to find the relation between x and y. Give answer
2) if x > y
3) if x < y
4) if x < y
5) if x = y or no relationship between x and y can be established
1.
I. 12x² - 55x + 63 = 0
II. 8y² - 22y + 15 = 0
2.
I. x² - 12x + 35 = 0
II. y ² - 14y + 48 = 0
3.
I. 6x² - 43x + 73 = 0
II. y² - 8y + 15 = 0
4.
I. 12x² - 31x + 20 = 0
II. y² - 12y + 32 = 0
5.
I. 2x² - 11x + 15 = 0
II. 2y² - 21y +40 = 0
Answer :
1. 1;
I. 12x² - 55x + 63 = 0
⇒ 12x² - 27x - 28 x +63 = 0
⇒ (3x-7) (4x-9) = 0
∴ x = 7/3, 9/4
II. 8y² - 22y + 15 = 0
⇒ 8y² - 10y - 12y + 15 = 0
⇒ (2y - 3) (4y-5) = 0
⇒ y = 3/2 , 5/4
Hence, x > y
2. 5;
I. x² - 12 + 35 = 0
⇒ x² - 5x - 7x + 35 = 0
⇒ (x-5) (x-7) = 0
∴ x = 5,7
II. y² - 14y + 48 = 0
⇒ y² -6y-8y + 48 = 0
⇒ (y-8) (y-6) = 0
∴ y = 8,6
∴ No relationship between x and y exists.
3. 5;
I. 6x² - 43x -72 = 0
⇒ 6x² - 16x - 27x + 72 = 0
⇒ (2x - 9) (3x - 8) = 0
∴ x = 9/2,8/3
II. y² - 8y + 15 = 0
⇒ y² - 3y - 5y + 15 = 0
⇒ (y-3) (y-5)
∴ y=3,5
∴ No relationship between x and y exists.
4. 3;
I. 12x² - 31x + 20 = 0
⇒ 12x² - 15x - 16x + 20 = 0
⇒ (3x-4) (4x-5) = 0
∴ x = 4/3, 5/4
II. y² - 12y + 32 = 0
⇒ y² - 4y - 8y +32 = 0
⇒ (y-8) (y-4) = 0
∴ y = 8,4
Hence, x < y
5. 5;
I. 2x² - 11x + 15 = 0
⇒ 2x² - 5x - 6x + 15 = 0
⇒ (x-3) (2x-5) = 0
∴ x = 3, 5/2
II. 2y² - 21y + 40 = 0
⇒ 2y² - 16y - 5y + 40 = 0
⇒ (2y-5) (y-8) = 0
∴ y =5/2,8
∴ No relationship between x and y exists.
