Aptitude Questions: Quadratic Equations Set 14

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Follow the link To solve Quadratic Equations with the help of Number Line

You have to solve equation I and II ,Give answer
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or cannot be established

1. I.5/x – 4/y = -2
   II.2/x + 3/y = 13
   
   Answer & Explanation

   Answer – 1)If X>Y
   Explanation :
   5u-4v = -2………*3 =>15u-12v = -6
   2u+3v = 13……..*4 => 8u+12v = 52
   Solve this eq
   23u = 46
   U=2, v=3
   X=1/2,y=1/3
   1/2 > 1/3….x > y
   
   
   
2. I.4X² + 4X – 3= 0
   II.14Y² – 17Y + 5 = 0
   
   Answer & Explanation

   Answer – 4)If X≤ Y
   Explanation :
   (2X-1)(2X+3) =0
   X=1/2, -3/2
   (2Y-1)(7Y-5) =0
   Y = 1/2, 5/7
   5/7, ½, ½, -3/2 => YYXX
   Y≥X
   
   
   
3. I.2X² – 17X + 36= 0
   II.Y² = 16
   
   Answer & Explanation

   Answer – 3)If X≥ Y
   Explanation :
   (2X-9)(X-4) =0
   X=9/2, 4
   Y = ±4
   9/2, 4,4,-4 => XXYY
   X≥Y
   
   
   
4. I.6X² + 19X + 15= 0
   II.3Y² + 11Y + 10 = 0
   
   Answer & Explanation

   Answer – 3)If X≥ Y
   Explanation :
   (3X+5)(2X+3) = 0
   X=-5/3, -3/2
   (Y+2)(3Y+5) =0
   Y = -2, -5/3
   -3/2, -5/3, -5/3, -2 => XXYY
   X≥ Y
   
   
   
5. I.4X² + 19X + 21= 0
   II.2Y² – 23Y + 63 = 0
   
   Answer & Explanation

   Answer – 1)If X>Y
   Explanation :
   (4x+7)(x+3) = 0
   X =-7/4, -3
   (2y+9)(y+7) = 0
   Y = -9/2, -7
   -7/4,-3, -9/2,-7 => xxyy
   x>y
   
   
   
6. I.3X² – 19X + 28= 0
   II.4Y² – 29Y + 45 = 0
   
   Answer & Explanation

   Answer – 5)If X=Y or cannot be established
   Explanation :
   (x-4)(3x-7) =0
   X=4,7/3
   (y-5)(4y-9) =0
   Y=5,9/4
   5,4,7/3,9/4 => yxyx
   
   
   
7. I.X² = 5625
   II.Y = ³√421875
   
   Answer & Explanation

   Answer – 4)If X≤ Y
   Explanation :
   X=±75
   Y =75
   x≤y
   
   
   
8. I.8X² + 22X + 15= 0
   II.4Y² + 16Y + 15 = 0
   
   Answer & Explanation

   Answer – 3)If X≥ Y
   Explanation :
   (4x+5)(2x+3) =0
   X=-5/4, -3/2
   (2y+5)(2xy+3) =0
   y=-5/2, -3/2
   -5/4,-3/2,-3/2,-5/3 => xxyy
   X≥Y
   
   
   
9. I.8X² + 10X + 3= 0
   II.5Y² – 8Y + 3 = 0
   
   Answer & Explanation

   Answer – 2)If X<Y
   Explanation :
   (2X+1)(4X+3) =0
   X= -1/2, -3/4
   (5Y-3)(Y-1) =0
   Y=1, 3/5
   3/5, 1, -1/2, -3/4
   YYXX => Y>X
   
   
   
10. I.3X + 2Y – 9= 0
    II.4Y – 15Y – 65 = 0
    
    Answer & Explanation

    Answer – 1)If X>Y
    Explanation :
    45X+30Y = 135
    8X-30Y=130
    53X=265
    X=5, Y= -3
    X>Y