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Given that \(x * y = \frac{x + y}{2}, x \circ y = ...

Given that xy=x+y2,xy=x2y and (3b)48=13, find b, where b > 0.

A.

8

B.

6

C.

5

D.

4

Correct answer is C

(xy)=x+y2

(3b)=3+b2

xy=x2y

(3+b2)48=(3+b2)248=13

(3+b)248×4=13

(3+b)2=48×43=64

b2+6b+9=64b2+6b+964=0

b2+6b55=0b25b+11b55=0

b(b5)+11(b5)=0(b5)=0 or (b+11)=0

Since b > 0, b - 5 = 0 

b = 5.