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Question 21

For real numbers $$a$$ and $$b$$, define $$a \ast b=\left(a+\frac{b}{2}\right)\left(b+\frac{a}{2}\right)$$. The value of $$(2 \ast 8)\ast2$$ is


Correct Answer: 1595

Solution

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First, $$2\ast8=(2+4)(8+1)=6 \times 9=54$$. Then $$54\ast2=(54+1)(2+27)=55 \times 29=1595$$.

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