Binary Operations in Real Numbers: Prove Associativity and Calculate Results

Math Problem Statement

Rezolva exercițiile incercuite

Solution

Vom rezolva exercițiile încercuite din imagine. Să începem cu C3 și C11.

C3:

Enunț: Pe $\mathbb{R}$ definim operația „ $*$ ” prin relația $x * y = xy - 2x - 2y + 6$ , pentru orice $x, y \in \mathbb{R}$ . Demonstrați că $3 * 3 = 2$ .

Soluție:

Conform definiției operației, avem

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Math Problem Analysis

Mathematical Concepts

Algebra
Binary Operations
Real Numbers
Associativity
Neutral Element

Formulas

x * y = xy - 2x - 2y + 6
x ⊙ y = (x + y)/2

Theorems

Associative property of binary operations
Existence of a neutral element

Suitable Grade Level

Grade 12

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