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Directions:1-10)**In the following questions, two equations I and II are given. You have to solve both the equations and g****ive Answer as,****In the following questions, two equations I and II are given. You have to solve both the equations and g****ive Answer as,**

1.

**√324 x + √11664 = 0****(16807)**^{1/5 }y + (9261)^{1/3}= 0

2.

- 2x – y = 31
- y = ∛19683

3.

- x
^{2}– 10x + 21 = 0 - y
^{2}– 10y + 16 = 0

4.

- 12x
^{2}– 17x – 57 = 0 - 4y
^{2}-7y – 36 = 0

5.

- 3x + 5y = 34
- 5x – 2y = 5

6.

- x
^{2}– 452 = 874 -√900 - y = (24+√(121+√(500+29)))

7.

- 3 + 18/x + 15/x
^{2}=0

2. 2 + 4/y+2/y^{2} =0

8.

- x
^{3}= 512

2. y^{2} – 17y + 72 =0

9.

- 9x+7y = 25

2. 5x+14y = 24

10.

- 15x
^{2}– 25x + 10 = 12x^{2}-6x -6 - 2y
^{2}+ 45y + 252 =0

**Check your Answers below:**

Directions:1-10)

**In the following questions, two equations I and II are given. You have to solve both the equations and g****ive Answer as,****ive Answer as,**- √324 x + √11664 = 0
- (16807)
^{1/5 }y + (9261)^{1/3}= 0

Ans:3

- √324 x + √11664 = 0

18x + 108 = 0

18x = -108

x = – 6

2. (16807)

^{1/5 }y + (9261)^{1/3}= 0(7

^{5})^{1/5}y + (21^{3})^{1/3}= 07y + 21 = 0

7y = -21

y = -3

Hence x < y

##### 2. Question

- 2x – y = 31
- y = ∛19683

Ans:1

- y = ∛19683

y = 27

2. 2x – y = 31

2x – 27 = 31

2x = 58

x = 29

Hence x > y

##### 3. Question

- x
^{2}– 10x + 21 = 0 - y
^{2}– 10y + 16 = 0

Ans:5

- x
^{2}– 10x + 21 = 0

(x – 7) (x – 3) = 0

x = 7, 3

2. y

^{2}– 10y + 16 = 0(y -8) (y – 2) = 0

y = 8, 2

Hence the relationship can’t be determined.

- x
##### 4. Question

- 12x
^{2}– 17x – 57 = 0 - 4y
^{2}-7y – 36 = 0

Ans:5

- 12x
^{2}– 17x – 57 = 0

12x

^{2}– 36x + 19x – 57 = 012x(x – 3) + 19(x – 3) = 0

(12x + 19) (x – 3) = 0

x = -19/12, 3

x = -1.58, 3

2.4y

^{2}-7y – 36 = 04y

^{2}-16y + 9y -36 = 04y(y – 4) + 9(y – 4) = 0

(4y + 9) (y – 4) = 0

y = -9/4, 4

y= -2.25, 4

- 12x

Hence the relationship can’t be determined.

- 12x
##### 5. Question

- 3x + 5y = 34
- 5x – 2y = 5

Ans:3

3x + 5y = 34 –à (1)5x – 2y = 5—à (2)By solving the equation (1) and (2), we get,

x = 3, y = 5

Hence x < y

##### 6. Question

- x
^{2}– 452 = 874 -√900 - y = (24+√(121+√(500+29)))

Ans:4

- x
^{2}– 452 = 874 -√900

x

^{2}= 1326 – 30 = 1296x =± 36

2. y = (24+√(121+23))

y = (24+12)

y = 36

**x ≤ y**y = (24+√(121+√(500+29)))

- x
##### 7. Question

- 3 + 18/x + 15/x
^{2}=0

2. 2 + 4/y+2/y

^{2}=0Ans:4

- 3 + 18/x + 15/x
^{2}=0

3x

^{2}+ 18x + 15 =03x

^{2}+ 3x + 15x +15 =03x (x+1) +15 (x+1) =0

(3x+15) (x+1) =0

x =-1, -15/3 = -1, -5

2. 2y

^{2}+ 4y + 2 =02y

^{2}+2y +2y +2 =02y (y+1) +2 (y+1) =0

(2y+2) (y+1) =0

y = -1, -2/2 = -1, -1

**x ≤ y**2 + 4/y+2/y

^{2}=0- 3 + 18/x + 15/x
##### 8. Question

- x
^{3}= 512

2. y

^{2}– 17y + 72 =0Ans:4

- x
^{3}= 512

x = 8

2. y

^{2}– 8y – 9y+ 72 =0(y-8) (y-9) =0

y = 8, 9

**x ≤ y**y

^{2}– 17y + 72 =0- x
##### 9. Question

- 9x+7y = 25

2. 5x+14y = 24

Ans:1

9x+7y = 25 —– (1)5x+14y = 24 —– (2)Simplify the above equation, we get x = 2 and y =1

**x > y**##### 10. Question

- 15x
^{2}– 25x + 10 = 12x^{2}-6x -6 - 2y
^{2}+ 45y + 252 =0

Ans:1

- 15x
^{2}– 25x + 10 = 12x^{2}-6x -6

3x

^{2}– 19x + 16 =03x

^{2}-3x – 16x + 16 =0(3x-16) (x-1) =0

x=16/3, 1 = 5.33, 1

2. 2y

^{2}+ 24y +21y + 252 =02y (y+12) + 21 (y+12) =0

(2y+21) (y+12) =0

y= -21/2, -12 = -10.5, -12

**x > y**2y^{2}+ 45y + 252 =0- 15x