Given the law of composition xoy=x+y+xy solve the equation (x^2-5)o3=-1.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We are given xoy = x + y + xy. We have to solve the equation (x^2 -  5)o3 = -1.

(x^2 -  5)o3 = -1

=> (x^2 - 5 + 3 + (x^2 - 5)3 = -1

=> x^2 + 2 + 3x^2 - 15 = -1

=> 4x^2 - 13 = -1

=> 4x^2  = 12

=> x^2 = 4

=> x = 2 and x = -2

The solution of the equation is x = 2 and x = -2

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To solve the equation, we'll have to use the given law of composition and to replace x and y by the terms (x^2 - 5) and 3.

(x^2 - 5)o3 = (x^2 - 5) + 3 + 3x^2 - 15

But (x^2 - 5)o3 = -1 => (x^2 - 5) + 3 + 3x^2 - 15 = -1

We'll remove the brackets and we'll shift all terms to one side:

x^2 - 5 + 3 + 3x^2 - 15 + 1 = 0

We'll combine like terms:

4x^2 - 16 = 0

We'll divide by 4:

x^2 - 4 = 0

x^2 = 4 => x1 = 2 and x2 = -2

The solutions of the equation are {-2 ; 2}.

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