Let a, x, y, z be real numbers satisfying the equations ax+ay=z x+ay=z x+ay=az, where x, y, z are not all zero, then the number of the possible values…

Question

Let a, x, y, z be real numbers satisfying the equations ax+ay=z x+ay=z x+ay=az, where x, y, z are not all zero, then the number of the possible values of a is

MARKS Content Team · Accepted Answer

Correct answer: 2. As x, y, z are not all zero, thus the system has a non-trivial solution. Thus, D=0 ⇒ a a -1 1 a -1 1 a -a =0 ⇒aa^2-a-aa-1+1a-a=0 or a^3-a^2-a^2+a=0 ⇒aa^2-2a+1=0 ⇒a=0, 1

Let $a, x, y, z$ be real numbers satisfying the equations
$a x + a y = z$
$x + a y = z$
$x + a y = a z,$ where
$x, y, z$ are not all zero, then the number of the possible values of $a$ is

Solution

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