Set-17 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 relation cannot be established

10.

Check your Answers below:

• Directions:1-5) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:If x > y

  1. Question

  I. X²+5 √3x -42 =0

  II. Y² -√2y -24 =0

  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x > y
  • If x = y or relation cannot be established
  Ans:5
  X²+5 √3 X -42 =0(X +7 √3) (X-2 √ 3) =0

  X =-7 √3,^, 2√3

  Y² – √2y -24 =0

  Y² – 4 √2y +3 √2y -24 =0

  Y = 4 √2, -3 √2

  The relationship cannot be determined

• 2. Question

  I. 5x – 2.2y = –17

  II. 4x + 0.6y = 31

  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x > y
  • If x = y or relation cannot be established
  Ans:2
  5x – 2.2y = –174x + 0.6y = 31

  Simply the above equation, we get x= 10 and y = 15

  x < y

• 3. Question

  I. 30×2+89x+58 =0

  II. 27y2 -51y -56 =0

  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x > y
  • If x = y or relation cannot be established
  Ans:2
  I. 30x²+89x +58 =030x² +60x + 29x +58 =0

  30x(x+2)+29 (x+2) =0

  (30x+29) (x+2) =0

  X = -29/30, -2

  II. 27y²-51y -56 =0

  27y² -72y + 21y -56 =0

  9y(3y -8) +7(3y-8) =0

  (9y+7)(3y-8) =0

  Y = -7/9, 8/3

  X < Y

• 4. Question

  I. X² -4x +3.91 =0

  II. Y²-6y +8.75 =0

  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x > y
  • If x = y or relation cannot be established
  Ans:2
  X² -4x +3.91 =0X²-2.3x – 1.7x +3.91 =0

  X(x-2.3) – 1.7 (x-3.91) =0

  (x-1.7)(x-2.3) =0

  X=2.3, 1.7

  Y²-6y +8.75 =0

  Y²-3.5y-2.5y+8.75 =0

  Y (y-3.5) – 2.5 (y-3.5) =0

  (y-3.5)(y-2.5)=0

  Y=3.5, 2.5

  x < y

• 5. Question

  I. 78x²+199x+65 =0

  II. 56y²+127y+72 =0

  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x > y
  • If x = y or relation cannot be established
  Ans:5
  I. 78x²+199x +65 =078x² +169x+30x +65 =0

  13x (6x+13) +5(6x+13) =0

  (13x+5) (6x+13) =0

  X= -5/13, -13/6

  II. 56y²+127y +72 =0

  56y² +64y+63y +72 =0

  8y (7y+8) +9(7y+8) =0

  (8y+9)(7y+8) =0

  Y= -9/8, -8/7

  Relationship cannot be determined.

  Directions: 6-10) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

  6. Question

  1. (x^1/4 /20)² = 196/X^3/2
  2. Y^1/3*y^2/3*14³ = 7*y⁴

  • If x > y
  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x = y or relation cannot be established
  Ans:5
  (x^1/4 /20)² = 196/X^3/2X^1/2/20² =196 / X^3/2

  X²=78400

  X = 280 , -280

  Y^1/3*y^2/3*14³ = 7*y⁴

  Y*14³=7 * y⁴

  14*14*14/7 =y³

  Y³= 196*2

  Y³ =392

  Y = 7.31 =7

  The relation cannot be established

• 7. Question

  1. 4/x^1/2 +7/x^1/2 = x^1/2
  2. Y² – (11^5/2/y^1/2) =0

  • If x > y
  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x = y or relation cannot be established
  Ans:5
  4/x^1/2 +7/ x^1/2 = x^1/211 =X

  Y² – (11^5/2/y^1/2) =0

  Y^5/2 =11^5/2

  Y =11

  x = y or relation cannot be established

• 8. Question

  1. 500^1/2x +402^1/2 =0
  2. 360^1/2y +200^1/2 =0

  • If x > y
  • If x < y
  • If x ≥ y
  • If x ≤ y
  • E. If x = y or relation cannot be established
  Ans:2
  500^1/2x +402^1/2 =0X = – (402/500)^1/2

  X = – 20/22 = -10/11

  360^1/2y +200^1/2 =0

  Y = – ( 200/360 )^1/2 = – 14/19

  x < y

• 9. Question

  1. X²-5 √3x -42 =0
  2. 4 √3 y² -5y -2 √3 =0

  • If x > y
  • If x < y
  • If x ≥ y
  • If x ≤ y
  • If x = y or relation cannot be established
  Ans:5
  X²+5 √3 X -42 =0(X +7 √3) (X-2√3) =0

  X =-7 √3 , 2√3

  4 √3Y² -5y -2 √3 =0

  Y = +8 /4√3 , -3 / 4 √3

  x = y or relation cannot be established

• 10. Question

  1. (x+40)^1/2 =256^1/2 – 121^1/2
  2. Y²+576 =697

  • If x > y
  • If x > y
  • If x ≥ y
  • If x ≤ y
  • If x = y or relation cannot be established
  Ans:2
  (x+40)^1/2 =256^1/2 – 121^1/2X+40 =25

  X=-15

  Y²+576 =697

  Y² =121

  Y =11 ,-11

  x < y