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Let be a binary operation on the set Q of all rational numbers given as

Question:

Let be a binary operation on the set $\mathrm{Q}$ of all rational numbers given as $\mathrm{a} * \mathrm{~b}=(2 \mathrm{a}-\mathrm{b})^{2}$ for all $\mathrm{a}, \mathrm{b} \in$ Q. Find $3 * 5$ and $5 * 3$. Is $3 * 5=5 * 3$ ?

 

Solution:

To find: $3 * 5$ and $5 * 3$

Given: $a * b=(2 a-b)^{2}$

$\Rightarrow 3 * 5=(6-5)^{2}=1$

Now $5^{*} 3=(10-3)^{2}=49$

$\Rightarrow 3 * 5$ is not equal to $5 * 3$

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