Đáp án và giải thích các bước giải:
`(x+{5-x}/{\sqrt[x]+1})^2+{16\sqrt[x](5-x)}/{\sqrt[x]+1}-16=0`
Có : `{16\sqrt[x](5-x)}/{\sqrt[x]+1}-16`
`={16(\sqrt[x]+1)(5-x)-16(5-x)}/{\sqrt[x]+1}-16`
`=-{16(5-x)}/{\sqrt[x]+1}-16x+64`
`PT⇔x^2+{(5-x)^2}/{(\sqrt[x]+1)^2}+{2x(5-x)}/{\sqrt[x]+1}+64-16x-{16(5-x)}/{\sqrt[x]+1}=0`
`⇔` `(x^2-16x+64)+{(5-x)^2}/{(\sqrt[x]+1)^2}+{2(x-8)(5-x)}/{\sqrt[x]+1}=0`
`⇔` `(x-8)^2+{(5-x)^2}/{(\sqrt[x]+1)^2}+{2(x-8)(5-x)}/{\sqrt[x]+1}=0`
`⇔` `(x-8+{5-x}/{\sqrt[x]+1})^2=0`
`⇔` `x-8+{5-x}/{\sqrt[x]+1}=0`
`⇔` `x-8={x-5}/{\sqrt[x]+1}`
`⇒` `x-5=(x-8)(\sqrt[x]+1)`
`⇔` `x-5=x\sqrt[x]+x-8\sqrt[x]-8`
`⇔` `x\sqrt[x]-8\sqrt[x]-3=0`
`⇔` `(\sqrt[x]-3)(x+3\sqrt[x]+1)=0`
Mà : `x+3\sqrt[x]+1>0`
`⇒` `\sqrt[x]-3=0`
`⇔` `\sqrt[x]=3`
`⇔` `x=9`
