Question

if alpha + beta = 2/7 and alpha × beta = 2/3 and are root of 3x²+4x-3=0 find the value of (1/alpha) + (1/beta)×(alpha⁴+beta⁴)
Hence show general formulae for alpha³ + beta³

Answer 1

Given equation 2x

3

−3x

2

+6x+1=0,

Sum of roots:

α+β+γ=

2

3

,

Product of roots:

αβγ=

2

−1

,

Sum of roots taken 2 at a time:

Σαβ=

2

6

=3

Now, we know that

(α+β+γ)

2

=α

2

+β

2

+γ

2

+2(αβ+βγ+γα)

Re-arranging, we get

α

2

+β

2

+γ

2

=(α+β+γ)

2

−2(Σαβ)

α

2

+β

2

+γ

2

=(

2

3

)

2

−2×3=

4

9

−6=−

4

15

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Answer 2

Answer:

Kiran Choudhary gave correct answer