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junior college 1 | H1 Maths
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Hi i need help checking my answers again! Thank you :)
Date Posted: 5 years ago
Views: 442
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x² - xy + y² = 1 ①
2x - y = k
So y = 2x - k ②
Sub ② into ①,
x² - x(2x - k) + (2x - k)² = 1
x² - 2x² + kx + 4x² - 4kx + k² = 1
3x² - 3kx + k² - 1 = 0
Since they meet at 2 distinct points,
Discriminant > 0
(-3k)² - 4(3)(k² -1) > 0
9k² - 12k² + 12 > 0
12 > 3k²
k² < 4
-2 < k < 2
Or
k² - 4 < 0
(k + 2)(k - 2) < 0
Positive coefficient of k means it's a u shaped curve.
So 2 < k < 2 for k² - 4 < 0 (below x axis)
2x - y = k
So y = 2x - k ②
Sub ② into ①,
x² - x(2x - k) + (2x - k)² = 1
x² - 2x² + kx + 4x² - 4kx + k² = 1
3x² - 3kx + k² - 1 = 0
Since they meet at 2 distinct points,
Discriminant > 0
(-3k)² - 4(3)(k² -1) > 0
9k² - 12k² + 12 > 0
12 > 3k²
k² < 4
-2 < k < 2
Or
k² - 4 < 0
(k + 2)(k - 2) < 0
Positive coefficient of k means it's a u shaped curve.
So 2 < k < 2 for k² - 4 < 0 (below x axis)
Thanks bro
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Date Posted:
5 years ago
Thank you!
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