If xy + yz + zx = 0, then1 + 1 + 1 (x, y, z ≠ 0) is

Home » Aptitude » Algebra » Question

If xy + yz + zx = 0, then 1 + 1 + 1 (x, y, z ≠ 0) is equal to:
x² − yz y² − zx z² − xy

x² − yz = x² − + xy + zx = x (x + y + z)
[∵ xy + yz + zx = 0
⇒ yz = −xy −zx]
Similarly,
y² − zx = y (x + y + z)
z² − xy = x (x + y + z)

∴ Expression =	1	+	1	+	1
	x(x + y + z)		y(x + y + z)		z(x + y + z)

=	yz + zx + xy	= 0
	xyz(x + y + z)

If xy + yz + zx = 0, then		1	+	1	+	1		(x, y, z ≠ 0) is equal to:
		x² − yz		y² − zx		z² − xy