Question

If m= 1 + √2 then find m⁴ - 1/m⁴​

Answer 1

Answer:

$m = 1 + \sqrt{2}$

$\frac{1}{m} = \frac{1}{1 + \sqrt{2} }$

$\frac{1}{m} = \sqrt{2} - 1$

${m}^{4} - { \frac{1}{m} }^{4}$

${ {m}^{2} }^{2} - { { \frac{1}{m} }^{2} }^{2}$

${ {(1 + \sqrt{2}) }^{2} }^{2} - { { \sqrt{2 - 1} }^{2} }^{2}$

Answer 2

Given :  m = 1  + √2

To Find : m⁴ - 1/m⁴  

Solution:

m = 1  + √2

Squaring both sides

=> m²  = 1 + 2 + 2√2

=> m²  = 3 + 2√2

m = 1  + √2

1/m  = 1/(1 +  √2)

=>1/m = √2 - 1

1/m²   = 2 + 1 - 2√2

=> 1/m² = 3 -  2√2

m⁴ - 1/m⁴  

= (m²  + 1/m²) (m² -  1/m²)

= (  3 + 2√2 +  3 -  2√2) ( 3 +  2√2  -  3 +  2√2)

= 6 (4√2)

= 24√2

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