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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.

I. X^{2}+5 √3x -42 =0

II. Y^{2} -√2y -24 =0

2.

I. 5x – 2.2y = –17

II. 4x + 0.6y = 31

3.

I. 30×2+89x+58 =0

II. 27y2 -51y -56 =0

4.

I. X^{2} -4x +3.91 =0

II. Y^{2}-6y +8.75 =0

5.

I. 78x^{2}+199x+65 =0

II. 56y^{2}+127y+72 =0

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.

**(x**^{1/4}/20)^{2}= 196/X^{3/2}**Y**^{1/3}*y^{2/3}*14^{3}= 7*y^{4}

7.

- 4/x
^{1/2}+7/x^{1/2}= x^{1/2} - Y
^{2}– (11^{5/2}/y^{1/2}) =0

8.

- 500
^{1/2}x +402^{1/2 }=0 - 360
^{1/2}y +200^{1/2 }=0

9.

- X
^{2}-5 √3x -42 =0 - 4 √3 y
^{2}-5y -2 √3 =0

10.

- (x+40)
^{1/2}=256^{1/2}– 121^{1/2} - Y
^{2}+576 =697

**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. X

^{2}+5 √3x -42 =0II. Y

^{2}-√2y -24 =0Ans:5

X^{2}+5**√**3 X -42 =0(X +7**√**3) (X-2**√**3) =0X =-7

**√**3,^{,}2**√**3Y

^{2 }–**√**2y -24 =0Y

^{2}– 4**√**2y +3**√**2y -24 =0Y = 4

**√**2, -3**√**2The relationship cannot be determined

##### 2. Question

I. 5x – 2.2y = –17

II. 4x + 0.6y = 31

Ans:2

5x – 2.2y = –174x + 0.6y = 31Simply 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

Ans:2

I. 30x^{2}+89x +58 =030x^{2}+60x + 29x +58 =030x(x+2)+29 (x+2) =0

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

X = -29/30, -2

II. 27y

^{2}-51y -56 =027y

^{2}-72y + 21y -56 =09y(3y -8) +7(3y-8) =0

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

Y = -7/9, 8/3

X < Y

##### 4. Question

I. X

^{2}-4x +3.91 =0II. Y

^{2}-6y +8.75 =0Ans:2

X^{2}-4x +3.91 =0X^{2}-2.3x – 1.7x +3.91 =0X(x-2.3) – 1.7 (x-3.91) =0

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

X=2.3, 1.7

Y

^{2}-6y +8.75 =0Y

^{2}-3.5y-2.5y+8.75 =0Y (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. 78x

^{2}+199x+65 =0II. 56y

^{2}+127y+72 =0Ans:5

I. 78x^{2}+199x +65 =078x^{2}+169x+30x +65 =013x (6x+13) +5(6x+13) =0

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

X= -5/13, -13/6

II. 56y

^{2}+127y +72 =056y

^{2}+64y+63y +72 =08y (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

**(x**^{1/4}/20)^{2}= 196/X^{3/2}**Y**^{1/3}*y^{2/3}*14^{3}= 7*y^{4}

Ans:5

(x^{1/4}/20)^{2}= 196/X^{3/2}X^{1/2}/20^{2}=196 / X^{3/2}X

^{2}=78400X = 280 , -280

Y

^{1/3}*y^{2/3}*14^{3}= 7*y^{4}Y*14

^{3}=7 * y^{4}14*14*14/7 =y

^{3}Y

^{3}= 196*2Y

^{3}=392Y = 7.31 =7

The relation cannot be established

##### 7. Question

- 4/x
^{1/2}+7/x^{1/2}= x^{1/2} - Y
^{2}– (11^{5/2}/y^{1/2}) =0

Ans:5

4/x^{1/2}+7/ x^{1/2}= x^{1/2}11 =XY

^{2}– (11^{5/2}/y^{1/2}) =0Y

^{5/2}=11^{5/2}Y =11

x = y or relation cannot be established

- 4/x
##### 8. Question

- 500
^{1/2}x +402^{1/2 }=0 - 360
^{1/2}y +200^{1/2 }=0

Ans:2

500^{1/2}x +402^{1/2 }=0X = – (402/500)^{1/2}X = – 20/22 = -10/11

360

^{1/2}y +200^{1/2 }=0Y = – ( 200/360 )

^{1/2}= – 14/19x < y

- 500
##### 9. Question

- X
^{2}-5 √3x -42 =0 - 4 √3 y
^{2}-5y -2 √3 =0

Ans:5

X^{2}+5**√**3 X -42 =0(X +7**√**3) (X-2**√**3) =0X =-7

**√**3 , 2**√**34

**√**3Y^{2}-5y -2**√**3 =0Y = +8 /4

**√**3 , -3 / 4**√**3x = y or relation cannot be established

- X
##### 10. Question

- (x+40)
^{1/2}=256^{1/2}– 121^{1/2} - Y
^{2}+576 =697

Ans:2

(x+40)^{1/2}=256^{1/2}– 121^{1/2}X+40 =25X=-15

Y

^{2}+576 =697Y

^{2}=121Y =11 ,-11

x < y

- (x+40)