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Mathematics
Jameson Bridges
10 June, 06:24
S the expression x3•x3•x3 equivalent to x3•3•3
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Katelynn Snyder
10 June, 08:32
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Remember
(x^m) (x^n) = x^ (m+n)
and difference of 2 perfect squres
(a²-b²) = (a-b) (a+b)
and sum or difference of 2 perfect cubes
so
(x^3) (x^3) (x^3) = x^ (3+3+3) = x^9
so
x^9=3*3*x^3
x^9=9x^3
minus 9x^3 both sides
0=x^9-9x^3
factor
0 = (x^3) (x^6-9)
factor difference of 2 perfect squraes
0 = (x^3) (x^3-3) (x^3+3)
factor differnce or sum of 2 perfect cubes (force 3 into (∛3) ³)
0 = (x³) (x-∛3) (x²+x∛3+∛9) (x+∛3) (x²-x∛3+∛9)
set each to zero
x³=0
x=0
x-∛3=0
x=∛3
x²+x∛3+∛9=0 has no solution
x+∛3=0
x=-∛3
x²-x∛3+∛9=0 has no solution
so the solutions are
x=-∛3, 0, ∛3
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