If the operation $⨁$ is defined by $a ⨁ b = a^{2} + b^{2}$ for all real numbers $a$ and $b$ , then $(2 ⨁ 3) ⨁ 4$ is equal to

120

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185

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175

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129

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312

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Solution

The correct option is B 185
Given, $a ⨁ b = a^{2} + b^{2}$
Therefore, $(2 ⨁ 3) ⨁ 4 = (2^{2} + 3^{2}) ⨁ 4$
$= (4 + 9) ⨁ 4 = 13 ⨁ 4$
$= (13)^{2} + (4)^{2} = 169 + 16 = 185$

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