Answer:
[tex]\frac{9}{4}[/tex]
Step-by-step explanation:
Given
x² - 3x
To make the expression a perfect square
add ( half the coefficient of the x- term )²
x² + 2( - [tex]\frac{3}{2}[/tex] )x + [tex]\frac{9}{4}[/tex], thus
x² - 3x + [tex]\frac{9}{4}[/tex]
= (x - [tex]\frac{3}{2}[/tex])² ← a perfect square
The value that must be added to the expression [tex]x^2- 3x[/tex] to make it a perfect square is (b) 9/4
The expression is given as:
[tex]x^2 - 3x[/tex]
Represent the coefficient of x with k.
So, we have:
[tex]k =-3[/tex]
Divide both sides of the equation by 2
[tex]\frac k2 =-\frac 32[/tex]
Take the square of both sides
[tex](\frac k2)^2 =(-\frac 32)^2[/tex]
Evaluate the squares
[tex](\frac k2)^2 =\frac 94[/tex]
Hence, the value that must be added to the expression [tex]x^2- 3x[/tex] to make it a perfect square is (b) 9/4
Read more about perfect squares at:
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