Question

If m=1+√2, then find the value of m⁴-1/m⁴​

Answer 1

Step-by-step explanation:

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

= {√2²+1²+2(√2)(1)} - {√2²+1²-2(√2)

= (2+1+2√2}{2+1-2-√2}

=(3+2√2)-(3-2-√2}

= 3+2√2-3+2√2

= 4√2

(1)}

m^-1/m² = (m²)² - (1/m²)²

= (m²-1/m²)(m²+1/m²)

= (4-√2) × 6

= 24√2

Answer 2

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