Let $a \bowtie b = a+\sqrt{b+\sqrt{b+\sqrt{b+...}}}$. If $7\bowtie g = 9$, find the value of

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Work Shown:

After subtracting 7 from both sides.

Note how because we have an infinite sequence of nested radicals, we can let which means x is equal to 2 as well.

This lets us say

Solve the equation for x to get

Since x is positive, this means we only focus on the first equation in the last line above.

Earlier we let x be equal to the infinite nested radicals involving g, but x is also equal to 2. So plug in x = 2 and use that to find g.

As a check, we can do the following

we're slowly approaching 9

its kinda hard to answer this when we dont have all the information that we need.