If {x^{2/3}} - 7{x^{1/3}} + 10 = 0, then x = | vedclass

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(D) Given the equation ${x^{2/3}} - 7{x^{1/3}} + 10 = 0.$This can be rewritten as ${({x^{1/3}})^2} - 7({x^{1/3}}) + 10 = 0.$Let $a = {x^{1/3}}.$ The e

Vedclass · Accepted Answer

${125, 8}$

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(D) Given the equation ${x^{2/3}} - 7{x^{1/3}} + 10 = 0.$This can be rewritten as ${({x^{1/3}})^2} - 7({x^{1/3}}) + 10 = 0.$Let $a = {x^{1/3}}.$ The equation becomes ${a^2} - 7a + 10 = 0.$Factoring the quadratic equation,we get $(a - 5)(a - 2) = 0.$Thus,$a = 5$ or $a = 2.$Since $a = {x^{1/3}},$ we have $x = {a^3}.$For $a = 5,$ $x = {5^3} = 125.$For $a = 2,$ $x = {2^3} = 8.$Therefore,the solution set is ${125, 8}.$

If ${x^{2/3}} - 7{x^{1/3}} + 10 = 0,$ then $x = $

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