The number of triples (x, y, z) such that any one of these numbers is added to the product of the other two, the result is 2, is
(a) 1
(b) 2
(c) 4
(d) infinitely many
Answers
The number of triples (x, y, z) = 1 such that any one of these numbers is added to the product of the other two, the result is 2
Step-by-step explanation:
The number of triples (x, y, z) such that any one of these numbers is added to the product of the other two, the result is 2, is
xy + z = 2 Eq1
xz + y = 2 Eq2
yz + x = 2 Eq3
Eq2 - Eq1
=> x(z - y) + y - z = 0
=> x(z - y) - (z - y) = 0
=> (x - 1) (z - y) = 0
=> x = 1 & y = z
Similarly using other two equations
we get y = 1 & x = z
& z = 1 & x = y
Hence x = y = z = 1
Triplet is ( 1 , 1 , 1)
The number of triples = 1 such that any one of these numbers is added to the product of the other two
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