Đáp án đây nhé nhật:
$\sqrt[3]{5x+7}- \sqrt[3]{5x-13}=1$ (1)
Đặt$\sqrt[3]{5x+7}=a$ ; $\sqrt[3]{5x-13}=b$
⇒a³=5x+7;b³=5x-13
⇒a³-b³=20⇒(a-b).(a²+ab+b²)=20 (2)
mặt khác : (1)⇔a-b=1⇔b=a-1 (3)
Từ (2),(3), ta có : 1.[a²+a.(a-1)+(a-1)²]=20
⇔a²+a²-a+a²-2a+1=20
⇔3a²-3a-19=0
⇔\(\left[ \begin{array}{l}a=\frac{3+\sqrt[]{237}}{6}\\a=\frac{3-\sqrt[]{237}}{6}\end{array} \right.\)
TH1:$a=\frac{3+\sqrt[]{237}}{6}$
⇒$\sqrt[3]{5x+7}=\frac{3+\sqrt[]{237}}{6}$
⇒5x+7=$\frac{90+11\sqrt[]{237}}{9}$
⇒5x=$\frac{27+11\sqrt[]{237}}{9}$
⇒x=$\frac{27+11\sqrt[]{237}}{45}$
TH2: $a=\frac{3=-sqrt[]{237}}{6}$
⇒5x-13=$\frac{90-11\sqrt[]{237}}{9}$
⇒5x=$\frac{207-11\sqrt[]{237}}{9}$
⇒x=$\frac{207-11\sqrt[]{237}}{45}$
