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

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Question

(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 $a = {x^{1/3}}$. Sub

Vedclass · Accepted Answer

${125, 8}$

Vedclass · Answer

(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 $a = {x^{1/3}}$. Substituting $a$ into the equation,we get the quadratic equation: ${a^2} - 7a + 10 = 0$.Factoring the quadratic equation: $(a - 5)(a - 2) = 0$.This gives the roots: $a = 5$ 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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