If m-1 ~m =5, find: m^2-1 ~m^2 - Vidyadip

Question

If $\mathrm{m}-\frac{1}{\mathrm{~m}}=5$, find: $\mathrm{m}^2-\frac{1}{\mathrm{~m}^2}$

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Answer

$ \mathrm{m}^2-\frac{1}{\mathrm{~m}^2}=\left(\mathrm{m}+\frac{1}{\mathrm{~m}}\right)\left(\mathrm{m}-\frac{1}{\mathrm{~m}}\right)$
$ =5\left(\mathrm{~m}+\frac{1}{\mathrm{~m}}\right)$
$ \text { Now }\left(\mathrm{m}+\frac{1}{\mathrm{~m}}\right)^2=\left(\mathrm{m}-\frac{1}{\mathrm{~m}}\right)^2+4$
$ =(5)^2+4$
$ =25+4$
$ =29$
$ \therefore \mathrm{m}+\frac{1}{\mathrm{~m}}=\sqrt{29}$
$ \therefore \mathrm{m}^2-\frac{1}{\mathrm{~m}^2}=(5)(\sqrt{29})=5 \sqrt{29}$

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