Question

If alpha beta and gamma are the roots of the equation x^3-x^2-1=0 then the value of (1+alpha)/(1-alpha)))

Answer 1

Step-by-step explanation:

Given If alpha beta and gamma are the roots of the equation x^3-x^2-1=0 then the value of (1+alpha)/(1-alpha)))

• So alpha, beta and gama are roots of equation x^3 – x^2 – 1 = 0
• Sum of the roots alpha + beta + gama = - b/a, alpha x beta x gama = - d/a and alpha beta + beta gama + alpha gama = c/a
• So α + β + γ = 1, αβγ = 1 and αβ + βγ + αγ = 0
• Now consider 1 + α / 1 – α + 1 + β / 1 – β + 1 + γ / 1 – γ
•     = (1 + α)(1 – β)(1 – γ) + (1 +β) (1 – α) (1 – γ) + (1 + γ)(1 – α)(1 – β) / (1 – α) (1-β) (1 – γ)
•    (1 + α – β – αβ – γ – αγ + βγ + αβγ) + (1 + β – α – αβ – γ – βγ + αγ + αβγ) + (1 + γ – α – αγ – β – βγ + αβ + αβγ) / (1 + α – β – αβ – γ – αγ + βγ + αβγ)
•    = 3 – (α + β + γ) – (αβ + βγ + αγ) + 3αβγ / 1 – (α + β + γ) – (αβ + βγ + αγ) – αβγ
•    = 3 – 1 – 0 + 3(1) / 1 – 1 + 0 – 1
•    = 5 / - 1
•   = - 5

Reference link will be

https://brainly.in/question/18385614