Question

if m=1+√2 then the value of m⁴-(1/m⁴) is​

Answer 1

Step-by-step explanation:

M = 1+√2

1/m = 1/1+√2

= 1/(1+√2) × (1-√2)/(1-√2)

= 1-√2/(1²-√2²)

= 1-√2/(1-2)

= 1-√2/-1

= -(1-√2)

= √2-1

m+1/m = √2+1+√2-1

= 2√2

m²+1/m² = (m+1/m)²-2(m)(1/m)

= (2√2)²-2

= 4(2)-2 = 8-2 = 6

m²-1/m² = (√2+1)² - (√2-1)²

= {√2²+1²+2(√2)(1)} - {√2²+1²-2(√2)(1)}

= {2+1+2√2}-{2+1-2√2}

= {3+2√2} - {3-2√2}

= 3+2√2-3+2√2

= 4√2

m⁴-1/m⁴ =

= (m²-1/m²)(m²+1/m²)

=4√2*6

=24√2