Algebra For SBI PO : Set

Algebra For SBI PO : Set – 25

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 relationship between x and y cannot be established

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I. 7x² – 9x + 2 = 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 relationship between x and y cannot be established

(d)

7x² – 7x – 2x + 2 = 0

or, 7x(x – 1) – 2(x – 1) = 0

(7x – 2) (x – 1) = 0

or, x = 2/7, 1

y² – y – 3y + 3 = 0

or, y(y – 1) – 3(y – 1) = 0

or, (y – 3) (y – 1) = 0

y = 1, 3

2) I. x² = 64

II) 2y² + 25y + 72 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(e)

x² = 64

x = ±8

2y² + 9y + 16y + 72 = 0

or, y(2y + 9) + 8(2y + 9) = 0

or, (y + 8) (2y + 9) = 0

∴y=-8, -9/2

3) I. x² + x – 20 = 0

2y² – 19y + 45 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(c)

x² + x – 20 = 0

or, x² + 5x – 4x – 20 = 0

or, x(x + 5) – 4(x + 5) = 0

or, (x – 4) (x + 5) = 0

x = 4, – 5

2y² – 10y – 9y + 45 = 0

or, 2y(y – 5) – 9(y – 5) = 0

or, (y – 5) (2y – 9) = 0

∴y=5, 9/2

4) I. 7x + 3y = 26

II) 2x + 17y = -41

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(a)

Eqn (I) × 2

Eqn (II) × 7

14x + 6y = 52

14x + 119y = – 287

– 113y = 339

y = – 3 and x = 5, ie x > y

5) I. 3x² – 20x + 33 = 0

2y² – 11y + 15 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(b)

3x² – 9x – 11x + 33 = 0

or, 3x(x – 3) – 11(x – 3) = 0

or, (3x – 11) (x – 3) = 0

x = 3, 11/3

2y² – 6y – 5y + 15 = 0

or, 2y(y – 3) – 5(y – 3) = 0

or, (y – 3) (2y – 5) = 0

∴y= 3, 5/2

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 relationship between x and y cannot be established.

6) I. 4x² – 43x + 105 = 0

II) 7y² – 29y + 30 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(a)

4x² – 28x – 15x + 105 = 0

or, 4x(x – 7) – 15(x – 7) = 0

or, (x – 7) (4x – 15) = 0

x = 7, 15/4

7y² – 14y – 15y + 30 = 0

or, 7y(y – 2) – 15(y – 2) = 0

or, (y – 2)(7y – 15) = 0

y = 2, 15/7

7) I. x² + 13x + 40 = 0

II) y² + 7y + 10 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(d)

x² + 8x + 5x + 40 = 0

or, x(x + 8) + 5(x + 8) = 0

or, (x + 5) (x + 8) = 0

x = – 5, – 8

II. y² + 2y + 5y + 10 = 0

or, y(y + 2) + 5(y + 2) = 0

or, (y + 2)(y + 5) = 0

y = – 2, – 5

8) I. x=∛2197

2y² – 54y + 364 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(d)

x = ∛2197

x = 13

II. 2y² – 28y – 26y + 364 = 0

or, 2y(y – 14) – 26(y – 14) = 0

or, (2y – 26) (y – 14) = 0

y = 14, 13

9. I. 5x² – 27x + 36 = 0

II) y² – 2y + 2 = 0

(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(a)

5x² – 15x – 12x + 36 = 0

or, 5x(x – 3) – 12(x – 3) = 0

or, (5x – 12) (x – 3) = 0

∴x= 12/5, 3

y² – y – 2y + 2 = 0

or, y(y – 1) – 2(y – 1) = 0

or, (y – 1)(y – 2) = 0

y = 1, 2

10) I. 13x – 8y + 81 = 0

II) 15x + 5y + 65 = 0(a) if x > y

(b) if x ≥ y

(c)if x < y

(d) if x ≤ y

(e) if x = y or relationship between x and y cannot be established

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(c)

eqn (I) × 5 + eqn (II) × 8

65x – 40y + 405 = 0

120x + 40y + 520 = 0

185x + 0 + 925 = 0

∴x= (-925)/185= -5

y= (13x+81)/8

= (-65+81 )/8= 16/8=2

x < y

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Algebra For SBI PO : Set – 24