Question

if m = 1+√2,then find the value of m power 4 - 1/m power 4​

Answer 1

Answer:

• The answer is 4.

Step-by-step explanation:

As given in the question,m = 1+ √2 and to find $\sf{m}^{4}$-$\sf\frac{1}{{m}^{4}}$

$\sf \implies \: {m}^{4} - \frac{1}{ {m}^{4} } \\ \\ \sf \: {( {m}^{2}) }^{2} - {( \frac{1}{ {m}^{2} }) }^{2} \\ \\ \sf \: ({m}^{2} + \frac{1}{ {m}^{2} } )( {m}^{2} - \frac{1}{ {m}^{2} } ) \\ \\ \sf \: (( {m + \frac{1}{m}) }^{2} - 2.m. \frac{1}{m} )((m + \frac{1}{m} )(m - \frac{1}{m} ) \\ \\ \\ \sf \: now \: put \: the \: value \: on \: their \: places \\ \\ \sf \: {(1 + \sqrt{2} + \frac{1}{1 + \sqrt{2} }) }^{2} - 2(1 + \sqrt{2} + \frac{1}{1 + \sqrt{2}} )(1 + \sqrt{2} - \frac{1}{1 + \sqrt{2} } )\\ \\ \sf \:((3 + \frac{1}{3} ) - 2) {(1 + \sqrt{2}) }^{2} \\ \\ \sf \: \frac{4}{3} \times 3 = 4$

Hence, the answer is 4.