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Determine the relation between x and y by solving the two quadratic equations.
I. x2 - 12x + 11 = 0
II. y2 = y
I. x2 - 12x + 11 = 0
II. y2 = y
- Ax < y
- Bx > y
- Cx = y OR the relationship cannot be determined.
- Dx ≤ y
Answer not set
Discussion 1
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CCommunity
I. x2 - 12x + 11 = 0
⇒ x2 - x - 11x + 11 = 0
⇒ x(x - 1) - 11(x - 1) = 0
⇒ (x - 11) (x - 1) = 0
⇒ x = +11 OR x = +1
II. y2 = y
⇒ y2 - y = 0
⇒ y(y - 1) = 0
⇒ y = 0 OR y = +1
So, when x = +1, x = y for y = 1 and x > y for y = 0
And when x = +11, x > y for y = 1 and x > y for y = 0
∴ x ≥ y.
⇒ x2 - x - 11x + 11 = 0
⇒ x(x - 1) - 11(x - 1) = 0
⇒ (x - 11) (x - 1) = 0
⇒ x = +11 OR x = +1
II. y2 = y
⇒ y2 - y = 0
⇒ y(y - 1) = 0
⇒ y = 0 OR y = +1
So, when x = +1, x = y for y = 1 and x > y for y = 0
And when x = +11, x > y for y = 1 and x > y for y = 0
∴ x ≥ y.