Answer:
A = 25 so that the expression [tex]x^2-10x+A[/tex] is a perfect-square trinomial.
Step-by-step explanation:
Given : expression [tex]x^2-10x+A[/tex]
We have to find the value of A so that each expression is a perfect-square trinomial.
perfect-square is the term in the form of [tex](a+b)^2 \ or\ (a-b)^2[/tex]
Since , we know the algebraic identity,
[tex](a+b)^2=a^2+b^2+2ab\\\\ (a-b)^2=a^2+b^2-2ab[/tex]
Given expression [tex]x^2-10x+A[/tex] is of the form of [tex](a-b)^2=a^2+b^2-2ab[/tex]
Thus, comparing , we get,
a= x ,
-2ab = -10x
⇒ b = 5
Thus adding b² term to get perfect-square trinomial.
b² = 25
Thus, the perfect-square trinomial becomes [tex]x^2-10x+25=(x-5)^2[/tex]
So, A = 25
