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junior college 1 | H1 Maths
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Date Posted: 3 years ago
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x₁ = (9x₀ + 26)¹/⁴ = ⁴√(9(2.5) + 26) = ⁴√48.5 ≈ 2.63898
x₂ = (9x₁ + 26)¹/⁴ = ⁴√(9(2.63898) + 26) = ⁴√(49.75082) ≈ 2.65583
x₃ = (9x₂ + 26)¹/⁴ = ⁴√(9(2.65583) + 26) = ⁴√(49.90247) ≈ 2.65785
x₄ = (9x₃ + 26)¹/⁴ = ⁴√(9(2.65785) + 26) = ⁴√(49.92065) ≈ 2.65809
x₅ = (9x₄ + 26)¹/⁴ = ⁴√(9(2.65809) + 26) = ⁴√(49.92281) ≈ 2.65812
x₆ = (9x₅ + 26)¹/⁴ = ⁴√(9(2.65812) + 26) = ⁴√(49.92308) ≈ 2.65812
Continuing, x₇ ≈ 2.65813 x₈ ≈ 2.65813, x₉ ≈ 2.65813
So the root is 2.65813 = 2.658 (4s.f)
x₂ = (9x₁ + 26)¹/⁴ = ⁴√(9(2.63898) + 26) = ⁴√(49.75082) ≈ 2.65583
x₃ = (9x₂ + 26)¹/⁴ = ⁴√(9(2.65583) + 26) = ⁴√(49.90247) ≈ 2.65785
x₄ = (9x₃ + 26)¹/⁴ = ⁴√(9(2.65785) + 26) = ⁴√(49.92065) ≈ 2.65809
x₅ = (9x₄ + 26)¹/⁴ = ⁴√(9(2.65809) + 26) = ⁴√(49.92281) ≈ 2.65812
x₆ = (9x₅ + 26)¹/⁴ = ⁴√(9(2.65812) + 26) = ⁴√(49.92308) ≈ 2.65812
Continuing, x₇ ≈ 2.65813 x₈ ≈ 2.65813, x₉ ≈ 2.65813
So the root is 2.65813 = 2.658 (4s.f)
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