Question : If $\mathrm{m}-\frac{1}{\mathrm{~m}}=7$, then what is the value of $\mathrm{m}^2+\frac{1}{\mathrm{~m}^2}$?
Option 1: 0
Option 2: 51
Option 3: 53
Option 4: 49
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Correct Answer: 51
Solution :
Given, $\mathrm{m}-\frac{1}{\mathrm{~m}}=7$
Squaring both sides,
⇒ $(\mathrm{m}-\frac{1}{\mathrm{~m}})^2=(7)^2$
⇒ $\mathrm{m^2}+\frac{1}{\mathrm{~m^2}}-2\times\mathrm{m}\times\frac{1}{\mathrm{~m}}=49$
⇒ $\mathrm{m^2}+\frac{1}{\mathrm{~m^2}}-2=49$
⇒ $\mathrm{m^2}+\frac{1}{\mathrm{~m^2}}=49+2=51$
Hence, the correct answer is 51.
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