Giải phương trình:
$10\sqrt{x^{6}+1}=3(x^{4}+2)$
click V cho chị vs ^^ –  Confusion 18-05-16 08:02 PM
vô nghiệm à –  Salim 16-05-16 04:22 PM
cai nay co nghiem dau –  boduongvidai 16-05-16 04:07 PM
Ta có:
PTTĐ: $10\sqrt{(x^2+1)(x^4-x^2+1)}=3[(x^4-x^2+1)+(x^2+1)](1)$
Đặt $\left\{ \begin{array}{l} \sqrt{x^2+1}=a\\ \sqrt{x^4-x^2+1}=b \end{array} \right.$
$\rightarrow (1)\Leftrightarrow 10ab=3(a^2+b^2)$
Đến đây thì ok r, e lm típ  nha! :D
Đặt $x^2=a(a\ge 0)$
Ta có $pt\iff 10\sqrt{a^3+1}=3(a^2+2)$
$\iff 10(\sqrt{a^3+1}-3a-3)=3a^2+6-30a-30$
$\iff \frac{10(a^3+1-9a^2-18a-9)}{\sqrt{a^3+1}+3a+3}=3a^2-30a-24$
$\iff \frac{10(a^3-9a^2-18a-8)}{\sqrt{a^3+1}+3a+3}=3(a^2-10a-8)$
$\iff \frac{10(a^2-10a-8)(a+1)}{\sqrt{a^3+1}+3a+3}=3(a^2-10a-8)$
$\iff (a^2-10a-8)(\frac{10(a+1)}{\sqrt{a^3+1}+3a+3}-3)=0$
Ta có: $a\ge 0=>\frac{10(a+1)}{\sqrt{a^3+1}+3a+3}-3<0$ (BD tương đương)
Vậy $a^2-10a-8=0\iff a=5+\sqrt{33}(do a\ge 0)=>x=\sqrt{5+\sqrt{33}},x=-\sqrt{5+\sqrt{33}} $
vậy hóa ra lúc đầu là đề sai. ko phải bấm nhầm @_@ –  nguyenquangtruonghktcute 16-05-16 08:20 PM
ban dang cach cua ban len cho moi nguoi theo doi voi, minh thay de nay cung dung ma, dau co gi sai dau –  tritanngo99 16-05-16 07:59 PM
bài này có cách nhanh hơn –  Salim 16-05-16 07:55 PM
mình ghi đề sai –  Salim 16-05-16 07:55 PM
à. bấm nhầm –  nguyenquangtruonghktcute 16-05-16 06:14 PM
mình bấm mt nó kêu vô nghiệm. thế mà vẫn có nghiệm á –  nguyenquangtruonghktcute 16-05-16 06:11 PM
tiếc nhỉ , k vote đc -_- –  ☼SunShine❤️ 16-05-16 06:08 PM

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