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3 years ago

Factor the binomial completely. x2−81

Mathematics

1 answer:

Nata [24]3 years ago

4 0

Answer:

(x - 9)(x + 9)

Step-by-step explanation:

x² - 81 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b), then

x² - 81

= x² - 9²

= (x - 9)(x + 9)

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Anna35 [415]

Answer:

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Step-by-step explanation:

Given

$y=c_1e^x +c_2e^{-x$

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Required

The solution

Differentiate $y=c_1e^x +c_2e^{-x$

$y' = c_1e^x - c_2e^{-x}$

Next, we solve for c1 and c2

$y(1) = 0$ implies that; x = 1 and y = 0

So, we have:

$y=c_1e^x +c_2e^{-x$

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$y'(1) =e$ implies that: x = 1 and y' = e

So, we have:

$y' = c_1e^x - c_2e^{-x}$

$e = c_1 * e^1 - c_2 * e^{-1}$

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Add (1) and (2)

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$e = 2c_1e$

Divide both sided by e

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Divide both sides by 2

$c_1 = \frac{1}{2}$

Substitute $c_1 = \frac{1}{2}$ in $0 = c_1 e + \frac{1}{e}c_2$

$0 = \frac{1}{2} e+ \frac{1}{e}c_2$

Rewrite as:

$\frac{1}{e}c_2 = -\frac{1}{2} e$

Multiply both sides by e

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So, we have:

$y=c_1e^x +c_2e^{-x$

$y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}$

$y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}$

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Answer:

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Step-by-step explanation:

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