Find the number that must be added to each expression to form a perfect square trinomial. Then write the trinomial as a binomial

Question

2 years ago

10

squared.

2 answers:

maksim [4K] · Answer 1 · 2022-03-24T03:43:12+03:00

8 0

<h2>Hello!</h2>

The answers are:

a) $\frac{49}{4}$

b) $(x+\frac{7}{2})^{2}$

First, we need to know that for this case:

$a=1\\2ab=7$

So,

$b=\frac{7}{2}$

$b^{2} =(\frac{7}{2})^{2}=\frac{49}{4}$

We must add $\frac{49}{4}$ to the expression in order to form a perfect square trinomial,

$x^{2} +7x+\frac{49}{4}$

Writing the trinomial as a binomial square:

$(x+\frac{7}{2})^{2}=x^{2}+2*\frac{7}{2}*x+(\frac{7}{2})^{2}=x^{2} +7x+\frac{49}{4}$

Have a nice day!

kaheart [24] · Answer 2 · 2022-03-24T05:53:43+03:00

Answer:

49/4 is the number.

Step-by-step explanation:

We have given the expression:

x²+7x+?

We have to find the number that must be added to form a perfect square trinomial.

(x+7/2)² = x+2(x)(7/2)+(7/2)²

(x+7/2)²

To form the expression perfect square 49/4 is added.

(x+7/2)² = x+2(x)(7/2)+(7/2)²= x+7x+49/4