Question

[Nguyễn Thị Diễm Quỳnh]

Gpt:

\(81x^4+5=3\sqrt[3]{108x^3+12x}\)

Các bạn cố gắng giúp mk câu này với!

Answer 1

[Hung nguyen]

Điều kiện: \(108x^3+12x\ge0\)

\(\Leftrightarrow x\ge0\)

Đặt \(3x=a\ge0\) thì ta có:

\(a^4+5=3\sqrt[3]{4a^3+4a}\)

\(\Leftrightarrow a^4-1=3\left(\sqrt[3]{4a^3+4a}-2\right)\)

\(\Leftrightarrow\left(a-1\right)\left(a+1\right)\left(a^2+1\right)=\dfrac{12\left(a^3+a-2\right)}{\sqrt[3]{\left(4a^2+4a\right)^2}+2\sqrt[3]{\left(4a^2+4a\right)}+4}\)

\(\Leftrightarrow\left(a-1\right)\left(a+1\right)\left(a^2+1\right)-\dfrac{12\left(a-1\right)\left(a^2+a+2\right)}{\sqrt[3]{\left(4a^2+4a\right)^2}+2\sqrt[3]{\left(4a^2+4a\right)}+4}=0\)

\(\Leftrightarrow\left(a-1\right)\left(\left(a+1\right)\left(a^2+1\right)-\dfrac{12\left(a^2+a+2\right)}{\sqrt[3]{\left(4a^2+4a\right)^2}+2\sqrt[3]{\left(4a^2+4a\right)}+4}\right)=0\)

\(\Leftrightarrow a=1\)

\(\Rightarrow3x=1\)

\(\Leftrightarrow x=\dfrac{1}{3}\)

Answer 2

[Lightning Farron]

sao ko liên hợp luôn cho chất .-.