Given the law of composition aob=2a+2b-1, solve the equation x03=x^2-10

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We'll replace the terms "a" and "b", from the given law of composition, by the terms x and 3.

xo3 = 2x + 2*3 -1

xo3 = 2x + 6 - 1

xo3 = 2x + 5 (1)

But, from enunciation, xo3 = x^2-10 (2)

We'll equate (1) and (2):

x^2-10 = 2x+5

We'll shift all terms to the left side:

x^2-10-2x-5=0

x^2-2x-15=0

We'll apply quadratic formula:

x1=[-(-2)+sqrt(4+60)]/2

x1=(2+8)/2

x1=10/2

x1=5

x2=(2-8)/2

x2=-6/2

x2=-3

**The set of solutions of the equation xo3 = x^2 - 10, is: {-3;5}.**

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