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Solve by cross multiplying. Check for extraneous solutions.

Solve by cross multiplying. Check for extraneous solutions.-example-1
User Grapsus
by
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1 Answer

2 votes

Answer:

x = 4; x = -4

Explanation:

Step 1: Cross multiply and simplify:

x * x = 2(x^2 - 8)

x^2 = 2x^2 - 16

Step 1: Subtract x^2 from both sides to set up the quadratic for solving:

(x^2 = 2x^2 - 16) - x^2

0 = x^2 - 16

Step 2: Add 16 to both sides:

(0 =x^2 - 16) + 16

16 = x^2

Step 3: Take the square root of both sides:

± √16 = √(x)^2

4 = x and -4 = x

Step 4: Check for extrraneous solutions by plugging in 4 and -4 for x in the original equations:

Plugging in 4 for x in x / (x^2 - 8) = 2 / x:

4 / (4^2 - 8) = 2 / 4

4 / (16 - 8) = 1/2

4 / 8 = 1/2

1/2 = 1/2

Plugging in 4 for x in x / (x^2 - 8) = 2 / x:

-4 / ((-4)^2 - 8) = 2 / -4

-4 / (16 - 8) = -1/2

-4 / 8 = -1/2

-1/2 = -1/2

Thus, there are no extraneous solutions so we can use x = 4 and x = -4 as the solutions.

User Davidforneron
by
8.3k points

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