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mr_godi [17]
3 years ago
14

Solve the equation. Identify any extraneous solutions.

Mathematics
2 answers:
Brrunno [24]3 years ago
6 0
x=\sqrt{2x+24}\\
x\geq 0 \wedge 2x+24\geq0\\
x\geq 0 \wedge 2x\geq-24\\
x\geq 0 \wedge x\geq-12\\
x\geq0\\\\
x=\sqrt{2x+24}\\
x^2=2x+24\\
x^2-2x-24=0\\
x^2+4x-6x-24=0\\
x(x+4)-6(x+4)=0\\
(x-6)(x+4)=0\\
x=6 \vee x=-4\\\\
-4\not \geq 0

So, <span>6 is a solution to the original equation. The value –4 is an extraneous solution.</span>

Mice21 [21]3 years ago
5 0
x=\sqrt{(2x+24)}\\\\The\ domain:\\2x+24\geq0\to x\geq-12\\x\geq0\\D:x\geq0\\\\x=\sqrt{2x+24}\ \ \ \ |square\ both\ sides\\\\x^2=(\sqrt{2x+24)})^2\\\\x^2=2x+24\ \ \ |-2x-24\\\\x^2-2x-24=0\\\\x^2+4x-6x-24=0\\\\x(x+4)-6(x+4)=0\\\\(x+4)(x-6)=0\iff x+4=0\ \vee\ x-6=0\\\\x=-4\notin D\ \vee\ x=6\in D

Answer: 6 is a solution to the original equation. The value –4 is an extraneous solution.

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The answer is Option B (x + 6)(x^2 + 8)

Step-by-step explanation:

Step 1: Group the given cubic polynomial into two sections.  

So  polynomial can be  grouped as

(x^3 + 6x^2) + (8x + 48)

Step 2:Find what's the common in each section.

In section (x^3 + 6x^2)  the come term is x^2

In section (8x + 48)  the come term is 8

Step 3:Factor the commonalities out of the two terms.

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Factoring out 8 from the second section(8x + 48) ,  we will get 8(x + 6).

Step 4: Combine the factors together for terms contains the same factor,

Combining we get,\left(x+6\right)\left(x^2+8\right)

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How to write an equation for the line perpendiculer and trhough the given ppoint?
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For m = slope of given line and (h, k) = given point, the perpendicular line will be
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Often, this equation can be simplified to another appropriate form, such as slope-intercept form (y = mx+b) or standard form (ax+by=c).

_____
The slope of a given line can be found by solving its equation for y. The slope is the coefficient of x in that solution. If the given line is characterized by two points, (x1, y1) and (x2, y2), then its slope is m = (y2-y1)/(x2-x1).

In the unusual case where the given line is vertical (x=<some constant>), the slope of the perpendicular line is zero, and the line you want becomes y=k.
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