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Hi. Please i need help with these . No jokes .

Question b : Find ;
the values of
1.alpha³+beta³ and 1/(alpha³) +1/(beta³)
2. the the equation whose roots are alpha³ and beta ³​

Hi. Please i need help with these . No jokes . Question b : Find ; the values of 1.alpha-example-1
User Nacross
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1 Answer

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Answer:

(a) 2, 6

(b) 155/8, -155, 8x² -155x -1 = 0

Explanation:

(a) The equation in standard form is ...

x^2 -(4+k)x +4k +1 = 0

Then the discriminant is ...

(4+k)^2 -4(1)(4k+1) = 4^2 +8k +k^2 -16k -4 = k^2 -8k +12 = (k -2)(k -6)

The roots are equal when the discriminant is zero. The values of k that make the discriminant be zero are k=2 and k=6.

__

(b) a^3 + b^3 = (a +b)(a^2 -ab +b^2) = (a+b)((a+b)^2 -3ab)

= (5/2)((5/2)^2 -3(-1/2)) = (5/2)(25/4 +3/2) = 155/8 = α³ +β³

1/a^3 +1/b^3 = (a^3 +b^3)/(ab)^3 = (155/8)/(-1/2)^3 = -155 = 1/α³ +1/β³

The desired equation can be written from ...

(x -a^3)(x -b^3) = 0

x^2 -(a^3 +b^3)x +(ab)^3 = 0

x^2 -155/8x -1/8 = 0 . . . . .substituting known values

8x^2 -155x -1 = 0

User Niels Billen
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