Best Answer:
cross multiply

you get -3v(v∧2-4v+4) = -24(v-2)

divide both sides by -3

==> v(v∧2-4v+4) = 8(v-2)

==> v^3 - 4v^2 +4v = 8v - 16

==>v^3 - 4v^2 +4v - 8v +16 = 0

==> v^3 - 4v^2 - 4v +16 = 0

now solve using calculator or factor theorem

let f(v) = v^3 - 4v^2 - 4v +16

try f(2), it = 2^3 - 4(2^2) - 4(2) +16 = 0

one of the solutions is v = 2

for others, divide f(v) by the factor you just got, (v-2)

v-2) v^3 - 4v^2 - 4v +16 ( v^2 - 2v -8

----- v^3 - 2v^2

----------------------------------

-2v^2 - 4v

-2v^2 +4v

---------------------------------

-8v + 16

-8v+16

------------------------

0

now find the zeroes for the quotient, v^2 - 2v -8

= (v +2) ( v - 4)

therefore the solution is v = 2, -2, 4

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