x^2/8=(8x)^(1/2)

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Solution for x^2/8=(8x)^(1/2) equation:


D( x )

8*x < 0

8*x < 0

8*x < 0

8*x+0 < 0 // - 0

8*x < 0 // : 8

x < 0/8

x < 0

x in <0:+oo)

(x^2)/8 = (8*x)^(1/2) // - (8*x)^(1/2)

(x^2)/8-(8*x)^(1/2) = 0

1/8*x^2-2*2^(1/2)*x^(1/2) = 0

t_1 = x^(1/2)

1/8*t_1^4-2*2^(1/2)*t_1^1 = 0

1/8*t_1^4-2*2^(1/2)*t_1 = 0

t_1*(1/8*t_1^3-2*2^(1/2)) = 0

1/8*t_1^3 = -(-2*2^(1/2)) // : 1/8

t_1^3 = 16*2^(1/2)

t_1^3 = 16*2^(1/2) // ^ 1/3

t_1 = 2*2^(1/2)

t_1 = 0

t_1 = 0

t_1 = 2*2^(1/2)

x^(1/2)-(2*2^(1/2)) = 0

x^(1/2)-2*2^(1/2) = 0

1*x^(1/2) = -(-2*2^(1/2)) // : 1

x^(1/2) = 2*2^(1/2)

x^(1/2) = 2*2^(1/2) // ^ 2

x = 8

t_1 = 0

x^(1/2)+0 = 0

x^(1/2) = 0

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

x^(1/2) = 0

x = 0

x in { 8, 0 }

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