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solong [7]
3 years ago
10

Find the values of a and b such that

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
3 0

Answer:

a = 1.5

b = 1.75

Step-by-step explanation:

First, we need to solve (x+a)^2 and replace the result in the initial equation as:

x^2+3x+4=(x+a)^2+b\\x^2+3x+4=x^2+2ax+a^2+b

Then, this equality apply only if the coefficient of x is equal in both sides and the constant is equal in both sides.

It means that we have two equations:

3x=2ax\\4=a^2+b

So, using the first equation and solving for a, we get:

3x=2ax\\3=2a\\a=\frac{3}{2}=1.5

Finally, replacing the value of a in the second equation and solving for b, we get:

4=a^2+b\\4=1.5^2+b\\b=4-1.5^2\\b=4-2.25\\b=1.75

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Step-by-step explanation:

Here's how I got it:

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