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100 36 Find the value of x. Leave your answer in simplest radical form. Type your answer...

100 36 Find the value of x. Leave your answer in simplest radical form. Type your-example-1
User Flupp
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1 Answer

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We will solve as follows:

We have that 100 is to sqrt(x^2+64^2) what 64 is to x, that is:


\frac{100}{\sqrt[]{x^2+64^2}}=(64)/(x)

Now, we solve for x:


100x=64\cdot\sqrt[]{x^2+64^2}

And simplifying, we will get:


10000x^2=4096(x^2+4096)\Rightarrow10000x^2=4096x^2+4096^2

Now, we operate like terms:


10000x^2-4096x^2=4096^2\Rightarrow x^2(10000-4096)=4096^2
\Rightarrow x^2(5904)=4096^2\Rightarrow x^2=(4096^2)/(5904)\Rightarrow x=\frac{1024}{3\sqrt[]{41}}

User Parrish Husband
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