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Alisiya [41]
3 years ago
10

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

squared.

Mathematics
2 answers:
maksim [4K]3 years ago
8 0
<h2>Hello!</h2>

The answers are:

a) \frac{49}{4}

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

<h2>Why?</h2>

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]3 years ago
5 0

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

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