Solve the following equations - xy ay-bx -c- xz az-cx -b- yz bz-cy -a-

Rewriting the given equations, we get ay+bx xy = 1 c , az+cz xz = 1 b , bz+cy yz = 1 a or a x + b y = 1 c , a x + c z = 1 b , b ...

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Equations Reducible to the Linear Form

Solve the fol...

Question

Solve the following equations :
$\frac{x y}{a y + b x} = c, \frac{x z}{a z + c x} = b, \frac{y z}{b z + c y} = a .$

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a^{3} (b z - c y)^{3} + b^{3} (c x - a z)^{3} + c^{3} (a y - b x)^{3} = 3 a b c (b z - c y) (c x - a z) (a y - b x)

b x + a y = c

c x + a z = b, c y + b z = a

\frac{a y - b x}{c} = \frac{c x - a z}{b} = \frac{b z - c y}{a}

\frac{x}{a} = \frac{y}{b} = \frac{z}{c}

a x + b y + c = 0

b x + c y + a = 0

c x + a y + b = 0

(b + c) x + (c + a) y + (a + b) z = 0

(c + a) x + (a + b) y + (b + c) z = 0

(a + b) x + (b + c) y + (c + a) z = 0

(a^{2} + b^{2} + c^{2} - b c - c a - a b) (x^{2} + y^{2} + z^{2}

- y z - z x - x y)

= (X^{2} + Y^{2} + Z^{2} - Y Z - Z X - X Y)

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