+249 Let \(a \bowtie b = a+\sqrt{b+\sqrt{b+\sqrt{b+...}}}\). If \(7\bowtie g = 9\), find the value of g.
+9673 \(7\bowtie g\\ = 7 + \sqrt{g+\sqrt{g+\sqrt{g+\cdot\cdot\cdot}}}\)
That means the whole thing after the 7 must be equal 2.
The dots means extended to infinity.
Therefore let \(x=\sqrt{g+\sqrt{g+\sqrt{g+\cdot\cdot\cdot}}}\)(it equals 2 at the same time.)
\(\sqrt{g+x} = x\\\sqrt{g+2} = 2\\ g + 2 = 4\\ g = 2\)
Finished!!
