I. 3x² – (6 + √5)x + 2√5 = 0
3x² – 6x – √5x + 2√5 = 0
3x (x – 2) – √5 (x – 2) = 0

(3x – √5) (x – 2) = 0

x =

II. 8y² – (16 + 3√5)y + 6√5 = 0
8y² – 16y – 3√5y + 6√5 = 0
8y (y – 2) – 3√5 (y – 2) = 0

(8y – 3√5) (y – 2) = 0
y = , 2

Hence, option E is correct.

𝐈. x² − 16x + 64 = 0

x² − 8x – 8x + 64 = 0

x(x − 8) − 8(x − 8) = 0

(x − 8) (x − 8) = 0

x = 8, 8

𝐈𝐈. y² − 16y + 63 = 0

y² − 7y – 9y + 63 = 0

y(y − 7) − 9(y − 7) = 0

(y – 9) (y – 7) = 0

y = 9, 7

so, No relation can be established between x and y.

𝐈. 25/x² − 15/x + 2 = 0

⇒ 2x² − 15x + 25 = 0

⇒ 2x² − 10x − 5x + 25 = 0

2x(x − 5) − 5(x − 5) = 0

(2x − 5)(x − 5) = 0

x = 5/2 , 5

𝐈𝐈. 40/y² + 1 = 13/y

⇒ y 2 − 13y + 40 = 0

⇒ y 2 − 8y − 5y + 40 = 0

⇒ y(y − 8) − 5(y − 8) = 0

(y − 5)(y − 8) = 0

y = 5, 8

so, x ≤ y

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