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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:**

1.

X^{2} -6 √3 X -48 =0

Y^{2 }– √2y -24 =0

2.

X^{2}+5 √3 X -42 =0

Y^{2} – 8 √2 y +30 = 0

3.

X^{2} +4 √10 x+40 =0

4 √3 Y^{2} -5y -2 √3 =0

4.

X^{2}– √2 x -24 =0

Y^{2} – 8 √3 y +48 =0

5.

2X^{2} – (4+√13) x +2 √13 =0

10y^{2} – (18+5 √13) y +9 √13 =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.

3x+5y =69

9x+4y =108

7.

63x -194x^{1/2}+143 =0

99y-255y^{1/2}+150=0

8.

12x^{2} + 11 x + 12 = 10x^{2}+22x

13y^{2} – 18y + 3 = 9y^{2} – 10y

9.

16x^{2} – 40x – 39 = 0

12y^{2} – 113y + 255 = 0

10.

(X^{1/4 })^{2}/625 =169/X^{3/2 }Y^{4/3}* Y^{2/3}*2786 =7*Y^{3}

**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:**##### 1. Question

X

^{2}-6 √3 X -48 =0

Y^{2 }– √2y -24 =0Ans:3

X^{2}-6**√**3 X -48 =0X(x -8**√**3) +2**√**3 (x -8**√**3) =0(X -8

**√**3) (x + 2**√**3) =0X =8

**√**3, – 2**√**3Y

^{2 }–**√**2y -24 =0Y

^{2}– 4**√**2y +3**√**2y -24 =0Y = 4

**√**2, – 3**√**2Relationship cannot be determined

##### 2. Question

X

^{2}+5 √3 X -42 =0

Y^{2}– 8 √2 y +30 = 0Ans:2

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

**√**3, 2**√**3Y

^{2}– 8**√**2y +30 = 0Y = 5

**√**2 , 3**√**2x < y

##### 3. Question

X

^{2}+4 √10 x+40 =0

4 √3 Y^{2}-5y -2 √3 =0Ans:2

X^{2}+4**√1**0 x + 40=0(X +2**√**10) (X +2**√**10) =0X= – 2

**√**10, – 2**√**104

**√**3 Y^{2}-5y -2**√**3 =0Y = +8 /4

**√**3, -3 / 4**√**3x < y

##### 4. Question

X

^{2}– √2 x -24 =0

Y^{2}– 8 √3 y +48 =0Ans:2

X^{2 }–**√**2X -24 =0X^{2}– 4**√**2X +3**√**2X -24 =0X = 4

**√**2 , -3**√**2Y

^{2}– 8**√**3 y +48 =0(Y -4

**√**3 ) (Y -4**√**3 ) =0Y =4

**√**3 , 4**√**3x < y

##### 5. Question

2X

^{2}– (4+√13) x +2 √13 =0

10y^{2}– (18+5 √13) y +9 √13 =0Ans:3

2X^{2}– (4+**√**13)x +2**√**13 =0X = 4 /2,**√**13/2X=2, 1.8

10y

^{2}– (18+5**√**13)y +9**√**13 =0Y = 18/10, 5

**√**13 /10Y =1.8, 1.8

x ≥ y

Directions:6-10)

##### 6. Question

3x+5y =69

9x+4y =108Ans:2

9x+4y =108 ——– (1)3x+5y =69 ——— (2)à(2)*3

9x+15y = 207

9x+4y =108

11y =99

Y=9

9x +36 =108

9x=72

X=8

x < y

##### 7. Question

63x -194x

^{1/2}+143 =0

99y-255y^{1/2}+150=0Ans:5

- 63x -194 x
^{1/2}+143 = 0

Or 63x -117 x

^{½ }-77 x^{½}+143 = 0Or (7 x

^{1/2}-13) (9 x^{1/2}-11) = 0x =169/ 49,121/81

- 99y – 255 y
^{½ }+150 = 0

or 99y – 165 y

^{1/2 }– 90 y^{1/2 }+150 = 0or (11y

^{1/2 }– 10)(9y^{1/2}-15) = 0y = 100/121, 225/81

- 63x -194 x
##### 8. Question

12x

^{2}+ 11 x + 12 = 10x^{2}+22x

13y^{2}– 18y + 3 = 9y^{2}– 10yAns:3

12x^{2}+ 11 x + 12 = 10x^{2}+22x2x^{2}-11x +12 =0X =8/2, 3/2 = 4, 1.5

13y

^{2}– 18y + 3 = 9y^{2}– 10y4y

^{2}-8y +3 =0Y = 6/4, 2/4 =1.5, 0.5

X≥ y

##### 9. Question

16x

^{2}– 40x – 39 = 0

12y^{2}– 113y + 255 = 0Ans:2

16x^{2}– 40x – 39 = 0or 16x^{2}– 52x + 12x – 39 = 0or (4x- 13) (4x + 3)

x= 13/4, – ¾

12y

^{2}– 113y + 255 = 0or 12y

^{2}– 45y – 68y + 255 = 0or (4y – 15) (3y – 17) = 0

y =15/4, 17/3

x < y

##### 10. Question

(X

^{1/4 })^{2}/625 =169/X^{3/2 }Y^{4/3}* Y^{2/3}*2786 =7*Y^{3}Ans:2

X^{1/2 }/625 =169/X^{3/2}X^{2 }= 625*169X= ± (25*13) = ±325

Y

^{6/3}*2786 =7*y^{3}Y =2786/7 =398

X<Y