Equation ProblemsPage 1
1.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X² + 13X + 42 = 0
2. Y² + 19Y + 90 = 0  (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X = Y 

Answer is: BSolve:
X² + 13X + 42 = 0
X² + 7X + 6X + 42 = 0
X(X + 7) + 6(X + 7) = 0
X = 7, 6
Again
Y² + 19Y + 90 = 0
Y² + 10Y + 9Y + 90 = 0
Y(Y + 10) + 9(Y + 10) = 0
Y = 10,9
So, X is greater than Y.
2.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X² + 15X + 56 = 0
2. Y²  23Y + 132 = 0  (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X = Y 

Answer is: ASolve:
X² + 15X + 56 = 0
X² + 8X + 7X + 56 = 0
X(X + 8) + 7(X + 8) = 0
X = 8, 7
Again
Y²  23Y + 132 = 0
Y²  12Y 11Y + 132 = 0
Y(Y  12) 11(Y 12) = 0
Y = 12, 11
So, Y > X, is true.
3.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X² + 7X + 12 = 0
2. Y² + 6Y + 8 = 0  (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X = Y 

Answer is: CSolve:
X² + 7X + 12 = 0
X² + 4X + 3X+ 12 = 0
X(X + 4) + 3(X + 4) = 0
(X + 4)(X + 3) = 0
X = 4, 3
Again
Y² + 6Y + 8 = 0
Y² + 4Y + 2Y + 8 = 0
Y(Y + 4) + 2(Y + 4) = 0
(Y + 4)(Y + 2) = 0
Y = 4, 2
So, X ≤ Y is right.
4.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X²  22X + 120 = 0
2. Y²  26Y + 168 = 0
 (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X = Y 

Answer is: CSolve:
X²  22X + 120 = 0
X²  12X 10X + 120 = 0
X(X  12) 10(X  12) = 0
(X  12)(X  10) = 0
X = 12, 10
Again
Y²  26Y + 168 = 0
Y²  14Y  12Y + 168 = 0
Y(Y  14)  12(Y  14) = 0
(Y 14)(Y  12) = 0
Y = 14, 12
So, X ≤ Y is right.
5.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X² + 12X + 32 = 0
2. Y² + 17Y + 72 = 0  (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X ≥ Y 

Answer is: DSolve:
X² + 12X + 32 = 0
X² + 8X + 4X+ 32 = 0
X(X + 8) + 4(X + 8) = 0
(X + 8)(X + 4) = 0
X = 8, 4
Again
Y² + 17Y + 72 = 0
Y² + 9Y + 8Y + 72 = 0
Y(Y + 9) + 8(Y + 9) = 0
(Y + 9)(Y + 8) = 0
Y = 9, 8
So, X ≥ Y is true.
6.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X²  4 = 0
2. Y² + 6Y + 9 = 0  (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X ≥ Y 

Answer is: BSolve:
X²  4 = 0
X = ± 2
Again
Y² + 6Y + 9 = 0
Y² + 3Y + 3Y + 9 = 0
Y(Y + 3) + 3(Y + 3) = 0
(Y + 3)(Y + 3) = 0
Y = 3, 3
So, X > y is true.
7.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X²  7X + 12 = 0
2. Y² + Y  12 = 0
 (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X ≥ Y 

Answer is: DSolve:
X²  7X + 12 = 0
X²  4X 3X + 12 = 0
X(X  4)  3(X  4) = 0
(X  4)(X  3) = 0
X = 4, 3
Y² + Y  12 = 0
Y² + 4Y  3Y  12 = 0
Y(Y + 4)  3(Y + 4) = 0
(Y + 4)(Y  3) = 0
Y = 4, 3
So, X ≥ Y is right.
8.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X² = 729
2. Y = √729
 (a)X < Y  (b)X > Y  (c)X ≤ Y  (d)X = Y 

Answer is: CSolve:
X² = 729
X = ± √729 = ± 27
Again
Y = √729
Y = 27