ĐKXĐ: $x≥0$
Đặt $x=y^{210}(y≥0)$ ta có PT:
$\sqrt[7]{y^{210}}-\sqrt[5]{y^{210}}=\sqrt[3]{y^{210}}-\sqrt[]{y^{210}}$
$⇔y^{30}-y^{42}=y^{70}-y^{105}$
$⇔y^{105}-y^{70}-y^{42}+y^{30}=0$
$⇔y^{30}(y^{75}-y^{40}-y^{12}+1)=0$
$⇔y^{30}[y^{40}(y^{35}-1)-(y^{12}-1)]=0$
$⇔y^{30}[y^{40}(y-1)(y^{34}+y^{33}+...+1)-(y-1)(y^{11}+y^{10}+...+1)]=0$
$⇔y^{30}[(y-1)(y^{74}+y^{73}+...+y^{40})-(y-1)(y^{11}+y^{10}+...+1)]=0$
$⇔y^{30}(y-1)(y^{74}+y^{73}+...+y^{40}-y^{11}-y^{10}-...-1)=0$
Tham khảo thôi nhé!(Không khuyến khích làm theo)
