A binary operation * defined on the set of real numbers \mathbb{R} is given by a * b = a^2… — JAMB UTME

A binary operation $*$ defined on the set of real numbers $\mathbb{R}$ is given by $a * b = a^2 + 2b - 5$ . If $3 * x = 12$ , what is the value of $x$ ?

Answer: 4

Answer

The value of

x

is 4.

Applying the binary operation definition

a * b = a^2 + 2b - 5

3 * x

gives

3^2 + 2x - 5 = 2x + 4

. Equating

2x + 4 = 12

yields

2x = 8

, so

x = 4

Step-by-Step Solution

Substitute

a = 3

and

b = x

into the operational rule

a * b = a^2 + 2b - 5

3 * x = 3^2 + 2x - 5 = 9 + 2x - 5 = 2x + 4

To express the operation

3 * x

as an algebraic expression in terms of

x

Set the simplified algebraic expression equal to the given value of 12.

2x + 4 = 12

The question states that

3 * x = 12

Solve the linear equation for

x

2x = 8 \implies x = 4

Subtract 4 from both sides and divide by 2.

Key Concept

Evaluating binary operations and solving algebraic equations involving defined operational rules.

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