If axy - byx - c- byz - czy - a- czx - axz - b- then find the value of yzx2 - zxy2 - xyz2

Writing the equations in a, b, c as under a(xy) + b(yx) c = 0 a b (yz) c(zy) = 0 a (xz) b+c (zx) = 0 #160;Eliminating a, b, c to get rela ...

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Factorisation Using Algebraic Identities

If axy + by...

Question

If $\frac{a x}{y} + \frac{b y}{x} = c, \frac{b y}{z} + \frac{c z}{y} = a, \frac{c z}{x} + \frac{a x}{z} = b,$ then find the value of $\frac{y z}{x^{2}} + \frac{z x}{y^{2}} + \frac{x y}{z^{2}}$

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\frac{x^{2} - y z}{a} = \frac{y^{2} - z x}{b} = \frac{z^{2} - x y}{c},

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

(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)

a^{2} + b^{2} + c^{2} = 2, x^{2} + y^{2} + z^{2} = 2

a, b, c, x, y, z > 0

If $a^{x - 1} = b c, b^{y - 1} = a c, c^{z - 1} = a b$ such that $x, y, z$ are integers then value of $x y + y z + z x - x y z$ is

a^{2} + b^{2} + c^{2} = 1

x^{2} + y^{2} + z^{2} = 1,

a, b, c, x, y, z \geq 0,

a x + b y + c z

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