pgt mathematics question solution

Question : Find pgt mathematics question solutionSolution ;\[\left|z-\frac{4}{z}\right|=2\] \[\left|\left|z\right|-\left|\frac{4}{z}\right|\right|\le\left|z-\frac{4}{z}\right|\] \[\left|\left|z\right|-\left|\frac{4}{z}\right|\right|\le2\] Let \[\left|z\right|=r\] \[\left|r-\frac{4}{r}\right|\le2\] \[-2\le r-\frac{4}{r}\le2\] First \[-2\le r-\frac{4}{r}r^2+2r-4\geq0\] roots are \[r=-1\pm\sqrt5\] \[r\le-1-\sqrt5\geq0 or r\geq-1+\sqrt5\] Since r>0 \[r\geq-1+\sqrt5 \] (1) now consider the right inequality \[r-\frac{4}{r}\le2\] \[r^2-2r-4\le0\]The roots are \[r=1\pm\sqrt5\] Thus…

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