Answer:
x =343 and x= - 125
Step-by-step explanation:
[tex]x^{\frac{2}{3} } - 35 = 2x^\frac{1}{3} }\\\\x^{\frac{2}{3} } - 2x^\frac{1}{3} }\ - 35 =0\\\\x^{\frac{1}{3} } = y\\\\y^{2} - 2y - 35 = 0\\\\(y-7)(y+5)=0\\\\y=7 , y = -5\\\\x^{\frac{1}{3} } = 7\\x=7^{3}\\and \\x^{\frac{1}{3} } = -5\\x= -5^{3}[/tex]
Check:
[tex]x^{\frac{2}{3}} -2x^{\frac{1}{3}} - 35 = 0\\ \\(7^{3})^{\frac{2}{3}} -2(7^{3})^{\frac{1}{3}} - 35 = 0\\\\7^{2}-2*7-35 =0 (true) , x=7^{3} =343\\\\((-5)^{3})^{\frac{2}{3}} -2(-5^{3})^{\frac{1}{3}} - 35 = 0\\\\(-5)^{2} -2*(-5)-35=0\\25 +10-35=0 (true), x=(-5)^{3} = -125[/tex]
