Question-217669

Question Number 217669 by MathWizz last updated on 17/Mar/25

Answered by SdC355 last updated on 18/Mar/25

x =^{10} \sqrt{m}

12 {(^{10} \sqrt{m})}^{7 / 5} + 3 {(^{10} \sqrt{m})}^{2 / 5} = 13 {(^{10} \sqrt{m})}^{9 / 10}

= 12 x^{14} - 13 x^{9} + 3 x^{4}

x^{4} (12 x^{10} - 13 x^{5} + 3) = 0

x^{4} (3 x^{5} - 1) (4 x^{5} - 3) = 0

x = 0

and x^{5} = \frac{1}{3} \to x = \frac{1}{^{5} \sqrt{3}}

and x^{5} = \frac{3}{4} \to x = \frac{^{5} \sqrt{3}}{^{5} \sqrt{4}}

x =^{10} \sqrt{m}

∴ m = 0 or \frac{1}{9} or \frac{9}{16}

Facebook Tweet Pin