4.1 Introduction: The Logic of Squares

Step 1

(i) Expand LHS: $(x-2)^2 + 1 = x^2 - 4x + 4 + 1 = x^2 - 4x + 5$ .

Step 2

Equate to RHS: $x^2 - 4x + 5 = 2x - 3$ .

Step 3

Rearrange: $x^2 - 6x + 8 = 0$ .

Step 4

This is of the form $ax^2+bx+c=0$ with $a=1 \neq 0$ . So, it is a quadratic equation.

Step 5

(ii) Expand LHS: $x^2 + x + 8$ .

Step 6

Expand RHS: $x^2 - 4$ (Difference of squares).

Step 7

Equate: $x^2 + x + 8 = x^2 - 4$ .

Step 8

Cancel $x^2$ : $x + 12 = 0$ .

Step 9

This is linear (degree 1), not quadratic.

Final Answer

(i) Yes, (ii) No

Input

Matrix

2×2

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