plz dear solve this math question brainliest yr ans awarded. spams will be reported
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plz dear solve this math question brainliest yr ans awarded. spams will be reported
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Question
If α and β are the roots of 2x² - x - 2 = 0, then (α⁻³ + β⁻³ + 2α⁻¹β⁻¹) is equal to
Solution
Since α and β are the roots of given equation, we have
α + β = 1/2 and αβ = -1
(Using, sum of zeroes = -b/a and product of zeroes = c/a for a quadratic equation of the form of ax² + bx + c)
Now,
α⁻³ + β⁻³ + 2α⁻¹β⁻¹ =
Now, use (x³ + y³) = (x + y)(x² + y² - xy)
Now,
α² + β² = (α + β)² - 2αβ
So, we get
Now put value of (α + β) and αβ
Hence the value of α⁻³ + β⁻³ + 2α⁻¹β⁻¹ is (-29/8)