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## Sagot :

1.

**Identify the coefficient of the linear term:**

The given expression is [tex]\( x^2 - 3x \)[/tex]. The coefficient of the linear term [tex]\( x \)[/tex] is -3.

2.

**Take half of the coefficient of [tex]\( x \)[/tex] and square it:**

The coefficient of [tex]\( x \)[/tex] is -3. Half of -3 is [tex]\( \frac{-3}{2} \)[/tex].

Squaring [tex]\( \frac{-3}{2} \)[/tex] gives:

[tex]\[ \left(\frac{-3}{2}\right)^2 = \frac{9}{4} \][/tex]

3.

**Add this squared value to the expression to complete the square:**

By adding [tex]\( \frac{9}{4} \)[/tex] to the expression [tex]\( x^2 - 3x \)[/tex], we turn it into a perfect square trinomial:

[tex]\[ x^2 - 3x + \frac{9}{4} \][/tex]

4.

**Rewrite the perfect square trinomial:**

This can be rewritten as:

[tex]\[ \left( x - \frac{3}{2} \right)^2 \][/tex]

Therefore, [tex]\( x^2 - 3x + \frac{9}{4} \)[/tex] is a perfect square trinomial.

**Conclusion:**

Thus, the value that must be added to [tex]\( x^2 - 3x \)[/tex] to make it a perfect square trinomial is [tex]\( \frac{9}{4} \)[/tex].

Therefore, the correct answer is [tex]\( \boxed{\frac{9}{4}} \)[/tex].