how-to-solve-x-1-1-3-x-3-1-3-x-5-1-3-0-

Question Number 85822 by jagoll last updated on 25/Mar/20

how to solve

\sqrt[3]{x - 1} + \sqrt[3]{x - 3} + \sqrt[3]{x - 5} = 0

Commented by jagoll last updated on 25/Mar/20

thank mr

Answered by john santu last updated on 25/Mar/20

Answered by TANMAY PANACEA. last updated on 25/Mar/20

w h e n a + b + c = 0

a^{3} + b^{3} + c^{3} = 3 a b c

(x - 1) + (x - 3) + (x - 5) = 3 {(x - 1)}^{\frac{1}{3}} {(x - 3)}^{\frac{1}{3}} {(x - 5)}^{\frac{1}{3}}

3 (x - 3) = 3 {(x - 1) (x - 3) (x - 5)}^{\frac{1}{3}}

{(x - 3)}^{3} = (x - 1) (x - 3) (x - 5)

(x - 3) {x^{2} - 6 x + 9 - (x - 1) (x - 5)} = 0

(x - 3) (x^{2} - 6 x + 9 - x^{2} + 6 x - 5) = 0

x = 3

Commented by jagoll last updated on 25/Mar/20

thank mr

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