Question

If m-1/m =1 find, m³-1/m³​

Answer 1

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Answer 2

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$\huge \rm {Answer:-}$

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$\rm {★Given:-}$

$\large \to \tt {m-\frac{1}{m}=1}$

$\rm {★To\: Find:-}$

$\large \to \tt {m^{3}-\frac{1}{m^{3}}=?}$

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$\large \dashrightarrow \tt {m-\frac{1}{m}=1}$

$\tt {★"cubing\: on\: both\: sides"}$

$\large \dashrightarrow \tt {(m-\frac{1}{m})^{3}=(1)^3}$

$\tt {★It\: is\: in\: the\: form\: of\: (a-b)^{3}}$

$\rm {★We\: know:-}$

$\tt \purple {(a-b)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}}$

$\large \dashrightarrow \tt {(m-\frac{1}{m})^{3}=(1)^3}$

$\large \dashrightarrow \tt {m^{3}-3(m)^{2}\times(\frac{1}{m})+3(m)\times(\frac{1}{m^{2}})-(\frac{1}{m^{3}})=1}$

$\large \dashrightarrow \tt {m^{3}-3\cancel{(m)^{2}}\times(\frac{1}{\cancel {m}})+3(\cancel{m})\times(\frac{1}{\cancel{m^{2}}})-(\frac{1}{m^{3}})=1}$

$\large \dashrightarrow \tt {m^{3}-3m+\frac{3}{m}-\frac{1}{m^{3}}=1}$

$\large \dashrightarrow \tt{m^{3}-\frac{1}{m^{3}}-3(m-\frac{1}{m})=1}$

$\large \dashrightarrow \tt{m^{3}-\frac{1}{m^{3}}-3(1)=1}$

$\tt{[∵ m-\frac{1}{m}=1]}$

$\large \dashrightarrow \tt{m^{3}-\frac{1}{m^{3}}-3=1}$

$\large \dashrightarrow \tt{m^{3}-\frac{1}{m^{3}}=1+3}$

$\large \dashrightarrow \tt{m^{3}-\frac{1}{m^{3}}=4}$

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$\rm {★Thence,}$

$\large \implies \tt \green{m^{3}-\frac{1}{m^{3}}=4}$

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