Question

if alpha and beta are the roots of the equation x^2 + 5x + 3 = 0, then find the value of 1/beta^3 - 1/ alpha^3.
please answer quickly it's important.

Answer 1

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Answer 2

Answer:

Given:

x2+5x+3=0  

The roots of the equation are  :α and β  

α+β=−ba  

⟹α+β=−5……..(1)  

α∗β=ca  

⟹α∗β=3……….(2)  

(α+β)2=α2+β2+2α∗β  

⟹(−5)2=α2+β2+2∗3[See(1) and (2)]  

⟹α2+β2=25–6  

⟹α2+β2=19………(3)  

Now,(α−β)2=α2+β2–2α⋅β  

⟹(α−β)2=19–6=13[See(3)]  

⟹α−β=±13−−√………(4)  

⟹1β3−1α3  

⟹α3−β3α3⋅β3  

⟹(α−β)(α2+α⋅β+β2)(α⋅β)3  

⟹(±13−−√)(19+3)33  

⟹22⋅±13−−√27

Step-by-step explanation:

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