Question

If m₁ and m₂ are slopes of lines represented by 6x² - 5xy + y² = 0, then (m₁)³ + (m₂)³ = ?

Options

• 9

• 15

• 27

• 35

Answer 1

35

Explanation:

Comparing the given equation with ax² + 2hxy + by² = 0, we get

a = 6, 2h = - 5, b = 1

`"m"_1 + "m"_2 = (-2"h")/"b" = 5`, m₁·m₂ = `"a"/"b"` = 6

`("m"_1)^3 + ("m"_2)^3 = ("m"_1 + "m"_2)("m"_1^2 - "m"_1"m"_2 + "m"_2^2)`

= 5 [(m₁ + m₂)² - 3m₁ m2]

= 5[(5)² - 3(6)]

= 5(7) = 35