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Determine the range of
(x² + x + 1)/(x² - x + 1)
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[tex]\huge\sf\fbox\purple{ Question }★ \\ [/tex]
❐Moderators
❐Brainly Stars
❐Other best users
Determine the range of
(x² + x + 1)/(x² - x + 1)
°°°° Don't Dare for Spam °°°°
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Step-by-step explanation:
Let y = (x2 + x + 1)/(x2 - x + 1)
⇒ x2y – xy + y = x2 + x + 1
⇒ x2y – xy + y – x2 – x – 1 = 0
⇒ x2(y – 1) – x(y + 1) + (y – 1) = 0
x is real ⇒ b2 – 4ac ≥ 0
⇒ (y + 1)2 – 4(y – 1)2 ≥ 0
⇒ (y + 1)2 – (2y – 2)2 ≥ 0
⇒ (y + 1 + 2y – 2) (y + 1 – 2y + 2) ≥ 0
⇒ (3y – 1) (–y + 3) ≥ 0 ⇒ –(3y – 1) (y – 3) ≥ 0 a=coeff. of y2 = –3 < 0.,But The expression ≥ 0
⇒ y lies between 1/3 and 3 ∴
Answer:
answer in the attachment
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