Set-4 Quadratic Equations (Inequalities) For SBI PO and SBI Clerk 2019 | Must Go Through These Questions

• If x > y
• If x ≥ y
• If x < y
• If x ≤ y
• If x = y or no relation can be established between ‘x’ and ‘y’.

9.

• Directions:1-10)In the following questions, two equations I and II are given. You have to solve both the equations and give Answer as,In the following questions, two equations I and II are given. You have to solve both the equations and give Answer as,

  1. √324 x + √11664 = 0
  2. (16807)^1/5 y + (9261)^1/3 = 0

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or the relation cannot be established

  Ans:3

  1. √324 x + √11664 = 0

  18x + 108 = 0

  18x = -108

  x = – 6

  2. (16807)^1/5 y + (9261)^1/3 = 0

  (7⁵)^1/5y + (21³)^1/3 = 0

  7y + 21 = 0

  7y = -21

  y = -3

  Hence x < y

• 2. Question

  1. 2x – y = 31
  2. y = ∛19683

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or the relation cannot be established

  Ans:1

  1. y = ∛19683

  y = 27

  2. 2x – y = 31

  2x – 27 = 31

  2x = 58

  x = 29

  Hence x > y

• 3. Question

  1. x² – 10x + 21 = 0
  2. y² – 10y + 16 = 0

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or the relation cannot be established

    Ans:5

  1. x² – 10x + 21 = 0

  (x – 7) (x – 3) = 0

  x = 7, 3

  2. y² – 10y + 16 = 0

  (y -8) (y – 2) = 0

  y = 8, 2

  Hence the relationship can’t be determined.

• 4. Question

  1. 12x² – 17x – 57 = 0
  2. 4y² -7y – 36 = 0

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or the relation cannot be established

  Ans:5

  1. 1. 12x² – 17x – 57 = 0

     12x² – 36x + 19x – 57 = 0

     12x(x – 3) + 19(x – 3) = 0

     (12x + 19) (x – 3) = 0

     x = -19/12, 3

     x = -1.58, 3

     2.4y² -7y – 36 = 0

     4y² -16y + 9y -36 = 0

     4y(y – 4) + 9(y – 4) = 0

     (4y + 9) (y – 4) = 0

     y = -9/4, 4

     y= -2.25, 4

  Hence the relationship can’t be determined.

• 5. Question

  1. 3x + 5y = 34
  2. 5x – 2y = 5

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or the relation cannot be established
  Ans:3
  3x + 5y = 34 –à (1)5x – 2y = 5—à (2)

  By solving the equation (1) and (2), we get,

  x = 3, y = 5

  Hence x < y

• 6. Question

  1. x² – 452 = 874 -√900
  2. y = (24+√(121+√(500+29)))

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or no relation can be established between ‘x’ and ‘y’.

  Ans:4

  1. x² – 452 = 874 -√900

  x² = 1326 – 30 = 1296

  x =± 36

  2. y = (24+√(121+23))

  y = (24+12)

  y = 36

  x ≤ y

  y = (24+√(121+√(500+29)))

• 7. Question

  1. 3 + 18/x + 15/x² =0

  2. 2 + 4/y+2/y² =0

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or no relation can be established between ‘x’ and ‘y’.

  Ans:4

  1. 3 + 18/x + 15/x² =0

  3x² + 18x + 15 =0

  3x² + 3x + 15x +15 =0

  3x (x+1) +15 (x+1) =0

  (3x+15) (x+1) =0

  x =-1, -15/3 = -1, -5

  2. 2y² + 4y + 2 =0

  2y² +2y +2y +2 =0

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

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

  y = -1, -2/2 = -1, -1

  x ≤ y

  2 + 4/y+2/y² =0

• 8. Question

  1. x³ = 512

  2. y² – 17y + 72 =0

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or no relation can be established between ‘x’ and ‘y’.

  Ans:4

  1. x³ = 512

  x = 8

  2. y² – 8y – 9y+ 72 =0

  (y-8) (y-9) =0

  y = 8, 9

                  x ≤ y

  y² – 17y + 72 =0

• 9. Question

  1. 9x+7y = 25

  2. 5x+14y = 24

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or no relation can be established between ‘x’ and ‘y’.
  Ans:1
  9x+7y = 25 —– (1)5x+14y = 24 —– (2)

  Simplify the above equation, we get x = 2 and y =1

  x > y

• 10. Question

  1. 15x² – 25x + 10 = 12x²-6x -6
  2. 2y² + 45y + 252 =0

  • If x > y
  • If x ≥ y
  • If x < y
  • If x ≤ y
  • If x = y or no relation can be established between ‘x’ and ‘y’.

  Ans:1

  1. 15x² – 25x + 10 = 12x²-6x -6

  3x² – 19x + 16 =0

  3x² -3x – 16x + 16 =0

  (3x-16) (x-1) =0

  x=16/3, 1 = 5.33, 1

  2. 2y² + 24y +21y + 252 =0

  2y (y+12) + 21 (y+12) =0

  (2y+21) (y+12) =0

  y= -21/2, -12 = -10.5, -12

  x > y2y² + 45y + 252 =0