If x^ 2/3 - 7 x^ 1/3 + 10 = 0, then x = - Vidyadip

MCQ

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

A
$\{125\}$
B
$\{8\}$
C
$\phi $
✓
$\{125, 8\}$

✓

Answer

Correct option: D.

$\{125, 8\}$

d
(d) Given that ${x^{2/3}} - 7{x^{1/3}} + 10 = 0$. Given equation can be written as

${({x^{1/3}})^2} - 7({x^{1/3}}) + 10 = 0$

Let $a = {x^{1/3}}$, then it reduces to the equation

${a^2} - 7a + 10 = 0\,\, \Rightarrow (a - 5)(a - 2) = 0\,\,\, \Rightarrow a = 5,\,2$

Putting these values, we have ${a^3} = x\,\,\,\, \Rightarrow x = 125$ and $8.$

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