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3-x-2-3-8x-16-16-x-




Question Number 10197 by konen last updated on 29/Jan/17
^3 (√(x−2))+^3 (√(8x−16))=16⇒x=?
$$\:^{\mathrm{3}} \sqrt{\mathrm{x}−\mathrm{2}}+^{\mathrm{3}} \sqrt{\mathrm{8x}−\mathrm{16}}=\mathrm{16}\Rightarrow\mathrm{x}=? \\ $$
Answered by sandy_suhendra last updated on 29/Jan/17
((x−2))^(1/3)   + ((8(x−2)))^(1/3)  = 16  ((x−2))^(1/3)  + 2((x−2))^(1/3)  = 16  3((x−2))^(1/3)  = 16  ((x−2))^(1/3)  = ((16)/3)  x−2 = (((16)/3))^3   x−2 = ((4096)/(27))  x = ((4150)/(27))
$$\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:\:+\:\sqrt[{\mathrm{3}}]{\mathrm{8}\left(\mathrm{x}−\mathrm{2}\right)}\:=\:\mathrm{16} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:+\:\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:=\:\mathrm{16} \\ $$$$\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:=\:\mathrm{16} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:=\:\frac{\mathrm{16}}{\mathrm{3}} \\ $$$$\mathrm{x}−\mathrm{2}\:=\:\left(\frac{\mathrm{16}}{\mathrm{3}}\right)^{\mathrm{3}} \\ $$$$\mathrm{x}−\mathrm{2}\:=\:\frac{\mathrm{4096}}{\mathrm{27}} \\ $$$$\mathrm{x}\:=\:\frac{\mathrm{4150}}{\mathrm{27}} \\ $$

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