5x^-1-2y^-1/-7x^-2-7y^-2

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Solution for 5x^-1-2y^-1/-7x^-2-7y^-2 equation: 


D( x )

x = 0

x = 0

x = 0

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

5*x^-1-(x^-2*((2*y^-1)/(-7)))-(7*y^-2) = 0

5*x^-1+(2/7)*x^-2*y^-1-7*y^-2 = 0

5*x^-1+2/7*x^-2*y^-1-7*y^-2 = 0

t_1 = x^-1

5*t_1^1+2/7*t_1^2*y^-1-7*y^-2 = 0

2/7*t_1^2*y^-1+5*t_1-7*y^-2 = 0

DELTA = 5^2-(-7*2/7*4*y^-2*y^-1)

DELTA = 8*y^-3+25

8*y^-3+25 = 0

8*y^-3 = -25 // : 8

y^-3 = -25/8

-3 < 0

1/(y^3) = -25/8 // * y^3

1 = -25/8*y^3 // : -25/8

-8/25 = y^3

y^3 = -8/25 // ^ 1/3

y = -(8/25)^(1/3)

DELTA = 0  <=>  t_2 = -(8/25)^(1/3)

t_1 = -5/(2/7*2*y^-1) i y = -(8/25)^(1/3)

t_1 = -35/4*y i y = -(8/25)^(1/3)

( t_1 = ((8*y^-3+25)^(1/2)-5)/(2/7*2*y^-1) or t_1 = (-(8*y^-3+25)^(1/2)-5)/(2/7*2*y^-1) ) i y > -(8/25)^(1/3)

( t_1 = 7/4*y*((8*y^-3+25)^(1/2)-5) or t_1 = -7/4*y*((8*y^-3+25)^(1/2)+5) ) i y > -(8/25)^(1/3)

y+(8/25)^(1/3) > 0

y+(8/25)^(1/3) > 0 // - (8/25)^(1/3)

y > -(8/25)^(1/3)

t_1 = -35/4*y

x^-1-(-35/4*y) = 0

x^-1+35/4*y = 0

1*x^-1 = -(35/4*y) // : 1

x^-1 = -35/4*y

-1 < 0

1/(x^1) = -35/4*y // * x^1

1 = -35/4*x^1*y // : -35/4*y

-4/35*y^-1 = x^1

x = -4/35*y^-1

t_1 = 7/4*y*((8*y^-3+25)^(1/2)-5)

t_3 = -7/4*y*((8*y^-3+25)^(1/2)-5)

t_3+x^-1 = 0

1*x^-1 = -t_3 // : 1

x^-1 = -t_3

-1 < 0

1/(x^1) = -t_3 // * x^1

1 = -t_3*x^1 // : -t_3

-t_3^-1 = x^1

x = -t_3^-1

t_1 = -7/4*y*((8*y^-3+25)^(1/2)+5)

t_4 = 7/4*y*((8*y^-3+25)^(1/2)+5)

t_4+x^-1 = 0

1*x^-1 = -t_4 // : 1

x^-1 = -t_4

-1 < 0

1/(x^1) = -t_4 // * x^1

1 = -t_4*x^1 // : -t_4

-t_4^-1 = x^1

x = -t_4^-1

x in { -4/35*y^-1, -(-7/4*y*((8*y^-3+25)^(1/2)-5))^-1, -(7/4*y*((8*y^-3+25)^(1/2)+5))^-1 }

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