Answer:
[tex]n=\dfrac{121}{4}[/tex]
Step-by-step explanation:
Given: [tex]x^2-11x+n[/tex]
The given expression is perfect square trinomial.
The middle term is negative.
[tex]a^2-2ab+b^2=(a-b)^2[/tex]
[tex]\Rightarrow x^2-11x+n[/tex]
[tex]\Rightarrow x^2-11x+n=a^2-2ab+b^2[/tex]
Compare both sides
[tex]a=x[/tex]
[tex]2ab=11x[/tex]
[tex]b^2=n[/tex]
Using three equation to solve for n
[tex]2xb=11x[/tex] [tex]\because a=x[/tex]
[tex]b=\dfrac{11}{2}[/tex]
Now, we will put b
[tex]n=b^2[/tex]
[tex]n=(\frac{11}{2})^2[/tex]
[tex]n=\dfrac{121}{4}[/tex]
Hence, The value of n is 121/4 which makes perfect square trinomial.
