## Algebra For SBI PO : Set – 21

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 no relation between ‘x’ and ‘y’ can be established.

1) I. 3x2 – 7x – 20 = 0

II. y2 – 8y + 16 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(d)

3x2 – 12x + 5x – 20 = 0

or 3x(x – 4) + 5(x – 4) = 0

or (3x + 5) (x – 4) = 0

∴x= -5/3,4

II. y2 – 8y + 16 = 0

or (y – 4)2 = 0

(y – 4) = 0

or y = 4

2) I. x2 – 72 = 0

II. y2 – 9y + 8 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(d)

x2 – 72 = 0

or x2 = 72

x = 8.485

II. y2 – y – 8y + 8 = 0

or y(y – 1) – 8(y – 1) = 0

or (y – 1) (y – 8) = 0

y = 1, 8

3) I. 9x2 – 114x + 361 = 0

II) y2 = 36

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(a)

9x2– l14x + 361 =0

or (3x – 19)2 = 0

3x – 19 = 0

∴x=19/3=6.33

y2 = 36

y = ±6

x > y

4) I. 13x + 17y = 107

II. x – 11y = – 41

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(c)

13x + 17y = 107 eqn (II) × 13

13x ± 143y = ± 533

160y = 640

∴y=640/160=4 and x=11y-41

x = 44 – 41 = 3

x < y

5) I. 9x2 + 18x + 9 = 0

II) y2 – 3y + 2 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(c)

9x2 + 18x + 9 = 0

or x2 + 2x + 1 = 0

or (x + l)2 = 0

x + 1 = 0, or x = -1

II. y2 – y – 2y + 2 = 0

or y(y – 1) -2(y – 1) = 0

or (y – 1) (y – 2) = 0

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 relation can be established between ‘x’ and y.

6) I. 4x + 7y = 42

II) 3x – 11y = – l

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(a)

eqn (I) ×3 – eqn (II) × 4

12x + 21y = 126

12x – 44y = -4

65y = 130

y = 2

and x = 7

7) I. 9x2 – 29x + 22 = 0

II) y2 – 7y + 12 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(c)

9x2 – 18x – 1 lx + 22 = 0

or 9x(x – 2)- 11(x – 2) = 0

or (x – 2)(9x – 11) = 0

∴x=2,11/9

II. y2 – 3y – 4y + 12 – 0

or y(y – 3) – 4(y – 3) = 0

or (y – 3) (y – 4) = 0

y = 3, 4

x < y

8) I. 3x2 – 4x – 32 = 0

II) 2y2 – 17y + 36 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(d)

3x2 – 4x – 32 = 0

or 3x2 – 12x + 8x – 32 = 0

or 3x(x – 4) + 8(x – 4) = 0

or (3x + 8) (x – 4) = 0

∴x=4, -8/3

II. 2y2 – 8y – 9y + 36 = 0

or 2y(y – 4) – 9(y – 4) = 0

or (2y – 9) (y – 4) = 0

or (2y – 9) (y – 4) = 0

∴y=4,9/2

9) I. 3x2 – 19x – 14 = 0

II) 2y2 + 5y + 3 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(a)

3x2 – 21x + 2x – 14 = 0

or 3x(x – 7) + 2(x – 7) = 0

or (3x + 2) (x – 7) = 0

x=7, -2/3

II. 2y2 + 5y + 3 = 0

or 2y2 + 2y + 3y + 3 = 0

or 2y(y + 1) + 3(y + 1) = 0

or (2y + 3) (y + 1) = 0

∴y=-3/2,-1

x > y

10) I. x2 + 14x + 49 = 0

II) y2 + 9y = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

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

(e)

x2 + 14x + 49 = 0

or (x + 7)2 = 0

x + 7 = 0

or, x = -7

II. y2 + 9y = 0

or y(y + 9) = 0

y = 0, -9

ie no relation between x and y.