Question

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​

Answer 1

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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