16x^2=81x^(2/3)

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Solution for 16x^2=81x^(2/3) equation:


x in (-oo:+oo)

16*x^2 = 81*x^(2/3) // - 81*x^(2/3)

16*x^2-(81*x^(2/3)) = 0

16*x^2-81*x^(2/3) = 0

t_1 = x^(2/3)

16*t_1^3-81*t_1^1 = 0

16*t_1^3-81*t_1 = 0

t_1*(16*t_1^2-81) = 0

16*t_1^2 = 81 // : 16

t_1^2 = 81/16

t_1^2 = 81/16 // ^ 1/2

abs(t_1) = 9/4

t_1 = 9/4 or t_1 = -9/4

t_1 = 0

t_1 = 0

t_1 = 9/4

x^(2/3)-9/4 = 0

1*x^(2/3) = 9/4 // : 1

x^(2/3) = 9/4

x^(2/3) = 9/4 // ^ 3

x^2 = 729/64 // ^ 1/2

abs(x) = 27/8

x = 27/8 or x = -27/8

t_1 = -9/4

x^(2/3)+9/4 = 0

1*x^(2/3) = -9/4 // : 1

x^(2/3) = -9/4

( -9/4 < 0 i 2/3 in (0:1) ) => x należy do O

t_1 = 0

x^(2/3)+0 = 0

x^(2/3) = 0

1*x^(2/3) = 0 // : 1

x^(2/3) = 0

x = 0

x in { 27/8, -27/8, 0 }

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