x^4/25=625/x^2

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Solution for x^4/25=625/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:0) U (0:+oo)

(x^4)/25 = 625/(x^2) // - 625/(x^2)

(x^4)/25-(625/(x^2)) = 0

(x^4)/25-625*x^-2 = 0

1/25*x^4-625*x^-2 = 0

t_1 = x^2

1/25*t_1^2-625*t_1^-1 = 0

(1/25*t_1^3-625*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1/25*t_1^3-625*t_1^0) = 0

t_1^1

(1/25)*t_1^3-625 = 0

(1/25)*t_1^3-625 = 0 // * 0

{ 1, -1, 5, -5, 25, -25, 125, -125, 625, -625, 3125, -3125, 15625, -15625 }

1

t_1 = 1

t_1^3-15625 = -15624

1

-1

t_1 = -1

t_1^3-15625 = -15626

-1

5

t_1 = 5

t_1^3-15625 = -15500

5

-5

t_1 = -5

t_1^3-15625 = -15750

-5

25

t_1 = 25

t_1^3-15625 = 0

25

t_1-25

t_1^2+25*t_1+625

t_1^3-15625

t_1-25

25*t_1^2-t_1^3

25*t_1^2-15625

625*t_1-25*t_1^2

625*t_1-15625

15625-625*t_1

0

t_1^2+25*t_1+625 = 0

DELTA = 25^2-(1*4*625)

DELTA = -1875

DELTA < 0

t_1 in { 25} 

t_1 = 25

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x in { 5, -5 }

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