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# If the operation $\oplus$ is defined by $a\oplus b={{a}^{2}}+{{b}^{2}}$ for all real numbers $a$ and $b$, then $(2\oplus 3)\oplus 4$ .

Last updated date: 12th Jul 2024
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Hint: We are given $a\oplus b={{a}^{2}}+{{b}^{2}}$ and we have to find $(2\oplus 3)\oplus 4$ . For that, first take $(2\oplus 3)$ and apply $a\oplus b={{a}^{2}}+{{b}^{2}}$. After that, the number we get from $(2\oplus 3)$ then apply it with $4$ . Try it, you will get the answer.

We take the set of numbers on which the binary operations are performed as $X$ . The operations (addition, subtraction, division, multiplication, etc.) can be generalized as a binary operation is performed on two elements (say $a$ and $b$) from set $X$ . The result of the operation on$a$and $b$ is another element from the same set $X$ .
Thus, the binary operation can be defined as an operation * which is performed on a set $A$. The function is given by *: $A*A\to A$ . So the operation * performed on operands $a$ and $b$is denoted by $a*b$ .
We are given, $a\oplus b={{a}^{2}}+{{b}^{2}}$ .
Now, $(2\oplus 3)\oplus 4$ ,
taking $(2\oplus 3)={{2}^{2}}+{{3}^{3}}=4+9=13$
Now, $13\oplus 4={{13}^{2}}+{{4}^{2}}=169+16=185$ .
So we get , $(2\oplus 3)\oplus 4=185$ .