## Algebra For SBI PO : Set – 28

D.1-5) : In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or If there is no relation between ‘x’ and ‘y’.

1) I. 2x2 – 21x + 54 = 0

II) y2 – 14y + 49 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or If there is no relation between ‘x’ and ‘y’. .

(c) I. 2x2 – 21x + 54 = 0

or 2x2 – 12x – 9x + 54 = 0

or 2x (x – 6) – 9 (x – 6) = 0

or (x – 6) (2x – 9) = 0 9

∴x=6, 9/2

II. y2 – 14y + 49 = 0

or (y – 7)2 = 0

or y – 7 = 0 y = 7 Hence x < y

2)I. x2 – 19x + 70 = 0

II. 2y2 – 17y + 35 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or If there is no relation between ‘x’ and ‘y’. .

(b)

x2 – 19x + 70 = 0 or x2 – 5x – 14x + 70 = 0

or x (x – 5) – 14 (x – 5) = 0

or (x – 5) (x – 14) = 0

x = 5, 14

2y2 – 10y – 7y + 35 = 0

or 2y (y – 5) – 7 (y – 5) = 0

or (y – 5) (2y – 7) = 0

y = 5,7/2
Hence x  y

3) I. 3x2 + 5x – 8 = 0

II) y2 – 4y + 3=0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or If there is no relation between ‘x’ and ‘y’. .

(d)

3x2 + 5x – 8 = 0

or 3x2 – 3x + 8x – 8 = 0

or 3x (x – 1) + 8 (x – 1) = 0

or (x – 1) (3x + 8) = 0

x = 1,-8/3

II. y2 – 4y + 3 = 0

or y2 – y – 3y + 3 = 0

or y (y – 1) – 3 (y – 1) = 0

or (y – l) (y – 3) = 0

y = 1, 3 Hence, x  y

4. I. 12x2 – 16x + 5 = 0

II) 18y2 – 45y + 25 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or If there is no relation between ‘x’ and ‘y’. .

(d)

12x2 – 16x + 5 = 0

or 12x2 – 6x – 10x + 5 = 0

or 6x(2x – 1) – 5(2x – 1) = 0

or (6x – 5) (2x – 1) = 0

x = ½ , 5/6

II. 18y2 – 45y + 25 = 0

or 18y2 – 30y – 15y + 25 = 0

or 6y (3y – 5) – 5 (3y – 5) = 0

or (3y – 5) (6y – 5) = 0

x = 5/3 , 5/6

5. I. 3x2 + 11x + 8 = 0

II) 3y2 + 20y + 32 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or If there is no relation between ‘x’ and ‘y’. .

(b)

3x2 + 11x + 8 = 0

or 3x2 + 3x + 8x + 8 = 0

or 3x(x+ 1) + 8(x + 1) = 0

or (x + 1) (3x + 8) = 0

∴x= -1,-8/3

II. 3y2 + 20y + 32 = 0

or 3y2 + 12y + 8y + 32 = 0

or 3y (y + 4) + 8 (y + 4) = 0

or (3y + 8) (y + 4) = 0

y = -4,-8/3

Hence, x ≥ y

D. 6-10) : In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established between ‘x’ and ‘y’.

6) I. x = ∛357911

II) y = √5041

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established between ‘x’ and ‘y’. .

(e)

x = ∛357911

x = 71

II. y = √5041

y = 71

x = y

7. I. 5x + 7y = -43

II) 9x – 17y = 41

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established between ‘x’ and ‘y’. .

(a)

Eqn (1) × 9 – Eqn (II) × 5

45x + 63y = -387

45x – 85y = 205

———————-

148 y = – 592

y = -4 and x = -3

x > y

8) I. x2+ 11x + 30 = 0

II) y2 + 9y + 20 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established between ‘x’ and ‘y’. .

(d)

x2 + 11x + 30 = 0 or x (x+5) + 6 (x+5) = 0

or (x + 5) (x + 6) = 0

x = -5, -6

II. y2 + 4y + 5y + 20 = 0

or y (y + 4) + 5 (y + 4) = 0

or (y + 4) (y + 5) = 0

y = -4,-5

x ≤ y

9. I. 4x2 + 3x – 1 = 0

II) 6y2 – 5y + l = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established between ‘x’ and ‘y’. .

a)

4x2 + 4x – x – 1 = 0

or 4x (x+ 1) – 1 (x + 1) = 0

or (4x – 1) (x + 1) = 0

x = -1, 1/4

II. 6y2 – 3y – 2y + 1 = 0

or 3y (2y – 1) – 1(2y – 1) = 0

or (3y – 1) (2y – 1) = 0

y =1/2 , 1/3

x < y

10) I. 3x2 + 15x + 18 = 0

II) 2y2 + 15y + 27 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established between ‘x’ and ‘y’. .

(b)

3x2 + 9x + 6x + 18 = 0 or 3x (x + 3) + 6 (x + 3) = 0

or (x + 3) (3+ 6) = 0

x = -3, -2

II. 2y2 + 6y + 9y+ 27 = 0

or 2y (y + 3) + 9 (y + 3) = 0

or (2y + 9) (y + 3) = 0

y = -3, -9/2