2510.21 – Defined Operation no. 2


Suppose aba \diamond b means ab+1ab + 1 and aba \bullet b means a+ba + b. Evaluate

4((68)(35)).4 \diamond ((6 \bullet 8) \bullet (3 \diamond 5)).


Solution

4((68)(35))=4((6+8)(35+1))=4(1416)=4(14+16)=430=430+1=121.\begin{aligned}4 \diamond ((6 \bullet 8) \bullet (3 \diamond 5)) &= 4 \diamond ((6 + 8) \bullet (3 \cdot 5 + 1))\\&= 4 \diamond (14 \bullet 16)\\&= 4 \diamond (14 + 16)\\&= 4 \diamond 30\\&= 4 \cdot 30 + 1\\&= 121.\end{aligned}