** Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-**

- I. 8/âˆšx + 9/(âˆšx +1) = 7,

II. 9/âˆšy â€“ 3/âˆšy = 2

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option B**

Solution:

8/âˆšx + 9/(âˆšx +1) = 7

[8(âˆšx +1) + 9âˆšx]/[âˆšx * (âˆšx +1)] = 7

17âˆšx + 8 = 7 (x + âˆšx)

7x – 10âˆšx â€“ 8 = 0

7x – 14âˆšx + 4âˆšx â€“ 8 = 0

7âˆšx (âˆšx â€“ 2) + 4 (âˆšx â€“ 2) = 0

âˆšx cannot be -4/7

So âˆšx = 2, so x = 4

9/âˆšy â€“ 3/âˆšy = 2

(9 – 3)/âˆšy = 2

Gives âˆšy = 3, so y = 9

- I. 9/âˆšx + 3/âˆšx = âˆšx + 1,

II. 4y^{2} + 5y â€“ 6 = 0

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option A**

Solution:

9/âˆšx + 3/âˆšx = âˆšx + 1

12/âˆšx = âˆšx + 1

x + âˆšx â€“ 12 = 0

x + 4âˆšx – 3âˆšx â€“ 12 = 0

âˆšx(âˆšx + 4) â€“ 3 (âˆšx + 4) = 0

âˆšx cannot be -4, So âˆšx = 3 => x = 9

4y^{2} + 5y â€“ 6 = 0

4y^{2} + 5y â€“ 6 = 0

Gives y = -2, 3/4

Put all values on number line and analyze the relationship

-2â€¦ 3/4â€¦ 9

- I. 6x
^{2} + 13x + 6 = 0,

II. 6y^{2} â€“ y â€“ 2 = 0

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option B**

Solution:

6x^{2} + 13x + 6 = 0

6x^{2} + 9x + 4x + 6 = 0

Gives x = -2/3, -3/2

6y^{2} â€“ y â€“ 2 = 0

6y^{2} + 3y â€“ 4y â€“ 2 = 0

Gives y = -1/2, 2/3

Put all values on number line and analyze the relationship

-3/2â€¦ -2/3â€¦ -1/2â€¦ 2/3

- I. 3x
^{2} + 14x â€“ 5 = 0,

II. 3y^{2} â€“ 11y + 6 = 0

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option B**

Solution:

3x^{2} + 14x â€“ 5 = 0

3x^{2} + 15x â€“ x â€“ 5 = 0

Gives x = -5, 1/3

3y^{2} â€“ 11y + 6 = 0

3y^{2} â€“ 9y â€“ 2y + 6 = 0

Gives y = 2/3, 3

Put all values on number line and analyze the relationship

-5â€¦ 1/3â€¦ 2/3â€¦ 3

- I. 6x
^{2} + 5x â€“ 1 = 0,

II. 3y^{2} â€“ 10y + 3 = 0

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option B**

Solution:

6x^{2} + 5x â€“ 1 = 0

6x^{2} + 6x â€“ x â€“ 1 = 0

Gives x = -1, 1/6

3y^{2} â€“ 10y + 3 = 0

3y^{2} â€“ 9y â€“ y + 3 = 0

Gives y = 1/3, 3

Put all values on number line and analyze the relationship

-1â€¦ 1/6â€¦ 1/3â€¦ 3

- I. 12x
^{2} â€“ 5x â€“ 3 = 0,

II. 3y^{2} â€“ 11y + 6 = 0

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option E**

Solution:

12x^{2} â€“ 5x â€“ 3 = 0

12x^{2} + 4x â€“ 9x â€“ 3 = 0

Gives x = -1/3, 3/4

3y^{2} â€“ 11y + 6 = 0

3y^{2} â€“ 9y â€“ 2y + 6 = 0

Gives y = 2/3, 3

Put all values on number line and analyze the relationship

-1/3â€¦ 2/3â€¦ 3/4â€¦ 3

- I. 6x
^{2} + 7x + 2 = 0,

II. 15y^{2} â€“ 38y â€“ 40 = 0

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option E**

Solution:

6x^{2} + 7x + 2 = 0

6x^{2} + 4x + 3x + 2 = 0

Gives x = -2/3, -1/2

15y^{2} â€“ 38y – 40 = 0

15y^{2} + 12y â€“ 50y – 40 = 0

Gives y = -4/5, 10/3

Put all values on number line and analyze the relationship

-4/5â€¦ -2/3â€¦ -1/2â€¦ 10/3

- I. 3x
^{2} â€“ 25x + 52 = 0,

II. 2y^{2} â€“ 7y + 3 = 0

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option A**

Solution:

3x^{2} – 25x + 52 = 0

3x^{2} – 12x â€“ 13x + 52 = 0

Gives x = 4, 13/3

2y^{2} â€“ 7y + 3 = 0

2y^{2} â€“ 6y â€“ y + 3 = 0

So y = 1/2, 3

Put all values on number line and analyze the relationship

1/2â€¦ 3â€¦ 4â€¦ 13/3

- I. x
^{2} = 1156,

II. y = âˆš1156

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option D**

Solution:

x^{2} = 1156,

So x = -34, 34

y = âˆš1156

So y = 34

Put all values on number line and analyze the relationship

-34â€¦ 34

- I. x
^{2} – âˆš3969 = âˆš6561,

II. y^{2} – âˆš1296 = âˆš4096

A) x > y

B) x < y

C) x â‰¥ y

D) x â‰¤ y

E) x = y or relation cannot be established

View Answer

** Option E**

Solution:

x^{2} – âˆš3969 = âˆš6561

x^{2} – 63 = 81

x^{2} = 144

So x = -12, 12

y^{2} – âˆš1296 = âˆš4096

y^{2} – 36 = 64

y^{2} = 100

So y = -10, 10

Put all values on number line and analyze the relationship

-12â€¦ -10â€¦.10â€¦. 12

tq

9âˆšx + 3/âˆšx = âˆšx + 1, check 2nd one it has mistake, but correct in solu

Yes divide symbol