Question

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

Answer 1

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}}`