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solve the equation, give steps!











































Use your knowledge of:

1. fractional exponents

2. negative exponents

Solve the following equation for x

0 = (1.5)x^0.5 - (0.5)x^-0.5

Comments for solve the equation, give steps!

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Mar 12, 2011
Solve the Equation
by: Staff


The question:

0 = (1.5)x^0.5 - (0.5)x^-0.5


The answer:

Before we start solving the equation, I’d like to review a couple of things:

First, x^0.5 is stands for x raised to the ½ power. x^0.5 means the square root of x.

Second, x^-0.5 is a negative exponent: x raised to the minus ½ power. x^-0.5 means 1 divided by the square root of x

x^-0.5 = 1/(x^+0.5)

Including the + sign is not necessary. I’ve included the + sign to make a point. This would normally be written as follows:

x^-0.5 = 1/(x^0.5)


Back to the equation:

0 = (1.5)x^0.5 - (0.5)x^-0.5

0 = (1.5)sqrt(x) - (0.5)/sqrt(x)


Multiply each side of the equation by sqrt(x)

0 * sqrt(x) = [(1.5)sqrt(x) - (0.5)/sqrt(x)] * sqrt(x)

0 = [(1.5)sqrt(x) - (0.5)/sqrt(x)] * sqrt(x)


Using the distributive law

0 = (1.5) * sqrt(x) * sqrt(x) – [(0.5)/sqrt(x)] * sqrt(x)


The sqrt(x) multiplied by the sqrt(x) = x

0 = (1.5) * x – [(0.5)/sqrt(x)] * sqrt(x)

0 = (1.5) * x – 0.5 * [sqrt(x)/sqrt(x)]


The sqrt(x) divided by the sqrt(x) = 1

0 = (1.5) * x – 0.5 * 1

0 = (1.5) * x – 0.5


Add 0.5 to each side of the equation

0 + 0.5 = (1.5) * x – 0.5 + 0.5

0.5 = (1.5) * x – 0.5 + 0.5

0.5 = (1.5) * x + 0

0.5 = (1.5) * x


Divide each side of the equation by 1.5

0.5/1.5 = (1.5) * x/1.5

1/3 = (1.5) * x/1.5

1/3 = (1.5/1.5) * x

1/3 = 1 * x

1/3 = x


The final answer is: x = 1/3


It’s a good idea to check the work. You can check this work by substituting 1/3 for x in the original equation and using a calculator.

0 = (1.5)x^0.5 - (0.5)x^-0.5

0 = (1.5)*(1/3)^0.5 - (0.5)*(1/3)^-0.5

0 = 0.866025 - 0.866025

0 = 0

Since 0 does = 0, the solution of x = 1/3 is correct.



Thanks for writing.


Staff
www.solving-math-problems.com



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