Question : If $(2x-y)^{2}+(3y-2z)^{2}=0$, then the ratio $x:y:z$ is:
Option 1: $1 : 3 : 2$
Option 2: $1:2:3$
Option 3: $3:1:2$
Option 4: $3:2:1$
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Correct Answer: $1:2:3$
Solution :
Given: $(2x - y)^2 + (3y - 2z)^2 = 0$
If the sum of squares of two terms is equal to zero, then the individual terms will also be zero.
Since, $(2x - y)^2 + (3y - 2z)^2 = 0$
$\therefore$ $2x - y = 0$ and $3y - 2z = 0$
$2x - y = 0$
$⇒ 2x = y$
$⇒ x:y = 1:2$
Also, $3y - 2z = 0$
$⇒ 3y = 2z$
$⇒ y:z = 2:3$
$\therefore$ $x:y:z = 1:2:3$
Hence, the correct answer is $1:2:3$.
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