Question

m^4/5 =0.32..find the value of m

Answer 1

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)² - (1/m²)² = (m²-1/m²)(m²+1/m²) = (4√2)² × 6 = 16(2) × 6 = 32 × 6 = 192