Question

if m is equal to 1 + root 2 then find the value of M raised to power 4 - 1 by m raised to power 4​

Answer 1

Solution:

It is given that,

i ) m = 1+√2 ------(1)

ii )1/m = 1/(√2+1)

Rationalising the denominator, we get

=> 1/m = (√2-1)/[(√2+1)(√2-1)]

=> 1/m = (√2-1)/[(√2)²-1²]

= (√2-1)/(2-1)

= √2-1 ----(2)

Now ,

iii )m+1/m = 1+√2+√2-1 = 2√2

iv) m-1/m = 1+√2-(√2-1)

= 1+√2-√2+1

= 2

v) m²+1/m² = (m+1/m)²-2

= (2√2)²-2

= 8-2

= 6

vi) m²-1/m² = (m+1/m)(m-1/m)

= 2√2 × 2

= 4√2

Now,

vii) m⁴ - 1/m⁴

= (m²)²-(1/m²)²

= (m²+1/m²)(m²-1/m²)

= 6 × 4√2

= 24√2

Therefore,

m⁴+1/m⁴ = 24√2

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