**Question: 8 (a) Find the value of a if (**

**a - 3**) = 10/a**(b) Find the value of X if 2**

**X**

*- 1 = 3*^{ 2}**X**

*- 2X*^{ 2}

Explore: (a )

(a-3) = 10/a

**=>**a(a-3) = 10

**=>**a

*-3a = 10*

^{ 2}**=>**a

*-3a - 10 = 0*

^{ 2}=> a

*-5a + 2a - 10 = 0*

^{ 2}=> a(a - 5) + 2(a - 5) = 0

=> (a -5) (a + 2) = 0

:. a - 5 = 0 Or, a + 2 = 0

=> a = 5 Or, => a = - 2

Answer: a = 5, - 2

(b) 2X

*- 1 = 3X*

^{ 2}*- 2X*

^{ 2}=> 2X

*-1 -3X*

^{ 2}*+ 2X = 0*

^{ 2}=> - X

*+ 2X - 1 = 0*

^{ 2}=> X

*-2X + 1 = 0*

^{ 2}=> X

*- 2.X.1 + 1*

^{ 2}*= 0*

^{ 2}=> (X -1)

^{ 2}

^{=> X = }^{1}

^{Answer: X = 1}

^{Question: 9 If X + Y = 1 & X - Y = 5, Then what X is equal to ?}

^{Option: (a) 2 (b) 4 (c) 5 (d) 3 (e) None}

^{ Explore:}

^{X+Y = 1}

^{X -Y = 5}

^{----------- [ Adding the equations]}

^{:. 2X = 6}

^{:. X =3}

^{Answer: X = 3}

^{Question: 10 If 2X - Y = 4 then 6X - 3y = ?}

^{Option: (a) 4 (b) 6 (c) 8 (d) 10 (e) 12}

^{Explore: At first it may occur to you that since we have two variables ( X,Y) we need two given equations to solve this problem. B ut not that you have not been asked to find out the values of X & Y. If you observe carefully, you will find that.}

^{ }

^{ 3 x (2X -Y) = 6X - 3Y}

^{Or, 3 x 4 - 6X - 3Y}

^{Or, 6X - 3Y = 12}

^{Answer: (e)}

^{Question: 11 If r = 12 & r/s = 24/Y, then /s = ?}

^{Option: (a) 0.5 (b) 2 (c) 3 (d) 4 (e) None}

^{Explore: r/s = 24/Y=> 12/s = 24/Y}

^{ Or, y/s = 24/12 = 2}

^{Answer: (b)}

^{Question: 12 If (3 - X)/ (1 + X) = 1, then X = ?}

^{Option: (a) 10 (b) 1 (c) 2 (d) -2 (e) None}

^{Explore: }

^{ (3 - X)/(1 + X) = 1}

^{Or, 3 - X = 1 + X }

^{Or, 3 - 1 = 2X}

^{Or, 2X = 2}

^{Or, X = 1}

^{Answer: (b)}

^{Question: 13 If X/Y = -1 and XY = -1, then X - Y =?}

^{Option: (a) 2 (b) 1 (c) 0 (d) -2 (e) None}

^{Explore: }

^{X/Y = -1 => X = - Y}

^{XY = -1 => (- Y) .Y = - 1}

^{Or, }y

*= 1*

^{ 2}^{:. Y = 1}

^{ }

**Question: 14 If**

**Y**+

^{ 2}**XY + 1 = 16 and X - Y = 1 then X + Y = ?**

Option: (a) -6 (b) 5 (c) 4 (d) 5 or -6 (e) None

^{ }

Explore: X - Y = 1 Or, X = 1 + Y

The other equation says

X

*+ XY + 1 = 16*

^{ 2}Or, (1 + Y)

*+ (1 + Y)Y + 1 = 16*

^{ 2}Or 1 + 2Y

*+ Y*

^{ 2}*+ 1 = 16*

^{ 2}Or, 2y

*+3y - 14 = 0*

^{ 2}Or, 2y

*+ 7Y - 4Y - 14 = 0*

^{ 2}Or y(2Y + 7) - 2(2Y + 7) = 0

Or, (2Y + 7)(Y - 2) = 0

:. 2Y + 7 = 0 => Y = -(7/2)

Or, y - 2 = 0 => y = 2

:. X = 1 + Y = 1 + 2 = 3 and X = 1 + Y = 1 - (7/2) = -(5/2)

:. X + Y = 3 + 2 = 5 and X + Y = -(5/2) -(7/2) = - 6

Answer: (d)