x2 ndash 15x 84 4x y2 ndash 15y 156 10y ........

Quantitative Aptitude ( CCS) Quadratic Equations

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x² – 15x + 84 = 4x

y² – 15y + 156 = 10y

x<=y

x>y

x>=y

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Explanation:

x² – 15x + 84 = 4x
⇒ x² – 19x + 84 = 0
⇒ x² – 12x – 7x + 84 = 0
⇒ x( x – 12) – 7 ( x – 12) = 0
⇒ (x – 7) (x – 12) = 0
⇒ x = 7, 12
y² – 15y + 156 = 10y
⇒ y² -25y + 156 = 0
⇒ y² – 12y – 13y + 156 = 0
⇒ y( y – 12) – 13 ( y – 12) = 0
⇒ (y – 13) (y – 12) = 0
⇒ y = 13, 12
∴ y ≥ x