Question

If m+ (1/m-2) = 4 find out (m-2) ^2 +1/(m-2) ^2 = ?

Answer 1

Question :-

$\sf{if \: \: (m - 2)+ \frac{1}{(m - 2)} = 4} \\ \sf{ then \: find \: the \: value \: of \: } \\ \sf{{(m - 2)}^{2} + \frac{1}{ {(m - 2)}^{2} } }$

Answer :-

$\red{\boxed{ \sf{ {(m - 2)}^{2} + \frac{1}{ {(m - 2)}^{2} } = 14}}} \:$

Formula used :-

$\rightarrow \: \boxed{\sf{ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}$

Solution :-

According to the question,

$\rightarrow \: \sf{ (m - 2) + \frac{1}{(m - 2)} = 4 }$

Squaring on both sides,

$\rightarrow \: \small \sf{{ \bigg((m - 2) + \frac{1}{(m - 2)} \bigg)}^{2} = {(4)}^{2} } \\ \\ \red{\bf{using \: the \: given \: formula \: } }\\ \\ \rightarrow \small \sf{{(m - 2)}^{2} + \frac{1}{ {(m - 2)}^{2} } + 2 \times (m - 2) \frac{1}{(m - 2)} = 16 }\\ \\ \rightarrow \: \sf{ \small {(m - 2)}^{2} + \frac{1}{ {(m - 2)}^{2} } + 2 = 16 }\\ \\ \rightarrow \boxed{ \sf{ {(m - 2)}^{2} + \frac{1}{ {(m - 2)}^{2} } = 14}}$