giai phuong trinh \(\sqrt{2x^2+11x+19}+\sqrt{2x^2+5x+7}=3\left(x+2\right)\)
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Những câu hỏi liên quan
giai phuong trinh : \(2x^2\left(5-\sqrt[3]{5x-x^3}\right)=2x^3+17x-8\)
giai phuong phuong trinh : \(\sqrt{2x^2+5x-3}-\sqrt{2x-1}=0\) 0
CM: \(|ab+cd|\subseteq\sqrt{\left(a^2+c^2\right)\left(b^2+d^2\right)}\)
giai cac phuong trinh
a)\(2x^4+5x^3+x^2+5x+2=0\)
b)\(\sqrt{x-1}-\sqrt[3]{2-x}=1\)
c)\(x-\sqrt{x}+1=\sqrt{2x^2-30x+2}\)
d)\(2x^2+3x+7=\left(x-5\right)\sqrt{2x^2+1}\)
e)\(\sqrt{x-2}+\sqrt{4-x}=2x^2-5x-1\)
Giai phuong trinh
1/ sqrt{x^2+4x+5}+sqrt{x^2-6x+13}3
2/ sqrt{3x^2-18x+28}+sqrt{4x^2-24x+45}6x-x^2-5
3/ sqrt{2x^2-4x+27}+sqrt{3x^2-6x+12}4x^2+8x+4
4/ sqrt{x^2+x+7}+sqrt{x^2+x+2}sqrt{3x^2+3x+19}
5/ left(x+2right)left(x+3right)-sqrt{x^2+5x+1}9
6/ left(x+4right)left(x+1right)-3sqrt{x^2+5x+2}6
7/ sqrt{2x^2+3x+5}+sqrt{2x^2-3x+5}3sqrt{x}
Đọc tiếp
Giai phuong trinh
1/ \(\sqrt{x^2+4x+5}+\sqrt{x^2-6x+13}=3\)
2/ \(\sqrt{3x^2-18x+28}+\sqrt{4x^2-24x+45}=6x-x^2-5\)
3/ \(\sqrt{2x^2-4x+27}+\sqrt{3x^2-6x+12}=4x^2+8x+4\)
4/ \(\sqrt{x^2+x+7}+\sqrt{x^2+x+2}=\sqrt{3x^2+3x+19}\)
5/ \(\left(x+2\right)\left(x+3\right)-\sqrt{x^2+5x+1}=9\)
6/ \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)
7/ \(\sqrt{2x^2+3x+5}+\sqrt{2x^2-3x+5}=3\sqrt{x}\)
Em xin phép làm bài EZ nhất :)
4,ĐK :\(\forall x\in R\)
Đặt \(x^2+x+2=t\) (\(t\ge\dfrac{7}{4}\))
\(PT\Leftrightarrow\sqrt{t+5}+\sqrt{t}=\sqrt{3t+13}\)
\(\Leftrightarrow2t+5+2\sqrt{t\left(t+5\right)}=3t+13\)
\(\Leftrightarrow t+8=2\sqrt{t^2+5t}\)
\(\Leftrightarrow\left\{{}\begin{matrix}t\ge-8\\\left(t+8\right)^2=4t^2+20t\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}t\ge\dfrac{7}{4}\\3t^2+4t-64=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}t\ge\dfrac{7}{4}\\\left(t-4\right)\left(3t+16\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}t\ge\dfrac{7}{4}\\\left[{}\begin{matrix}t=4\left(tm\right)\\t=-\dfrac{16}{3}\left(l\right)\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow x^2+x+2=4\)\(\Leftrightarrow x^2+x-2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
Vậy ....
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giai phuong trinh:
\(\left(\sqrt{x+4}-2\right)\left(\sqrt{4-x}+2\right)=2x\)
ĐKXĐ : \(-4\le x\le4\)
TA CÓ : \(\left(\sqrt{x+4}-2\right)\left(\sqrt{4-x}+2\right)=2x\)
\(\Leftrightarrow\left[\left(\sqrt{x+4}-2\right)\left(\sqrt{x+4}+2\right)\right]\left(\sqrt{4-x}+2\right)=2x\left(\sqrt{x+4}+2\right)\)
\(\Leftrightarrow\left[x+4-4\right]\left(\sqrt{4-x}+2\right)-2x\left(\sqrt{x+4}+2\right)=0\)
\(\Leftrightarrow x\left(\sqrt{4-x}+2\right)-2x\left(\sqrt{x+4}+2\right)=0\)
\(\Leftrightarrow x\left[\sqrt{4-x}+2-2\sqrt{x+4}-4\right]=0\)
\(\Leftrightarrow x=0\)HOẶC \(\sqrt{4-x}-2\sqrt{x+4}-2=0\)
VỚI \(\sqrt{4-x}-2\sqrt{x+4}-2=0\)
\(\Leftrightarrow\sqrt{4-x}-2=2\sqrt{x+4}\)
\(\Leftrightarrow4-x+4-4\sqrt{4-x}=4x+16\)
\(\Leftrightarrow8-x-4x-16=4\sqrt{4-x}\)
\(\Leftrightarrow-5x-8=4\sqrt{4-x}\)ĐK : \(-4\le x\le\frac{-8}{5}\)
\(\Leftrightarrow\left[-\left(5x+8\right)\right]^2=16\left(4-x\right)\)
\(\Leftrightarrow25x^2+64+80x=64-16x\)
\(\Leftrightarrow25x^2+96x=0\Leftrightarrow x\left(25x+96\right)=0\)
\(\Leftrightarrow x=0\)HOẶC \(x=\frac{-96}{25}\)(THỎA MÃN ĐK )
VẬY PT CÓ 2 NGHIỆM \(x\in\left[0;\frac{-96}{25}\right]\)
P/S : CÁCH CỦA MÌNH KHÁ DÀI VÀ CHI TIẾT QUÁ . BẠN CÓ THỂ THAM KHẢO CÁCH KHÁC NHANH HƠN :>
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1) giai phuong trinh:
a) \(x+\sqrt{2x+3}=2x\left(x-2\right)\)
Lời giải:
ĐK: $x\geq \frac{-3}{2}$
PT $\Leftrightarrow \sqrt{2x+3}=2x^2-5x$
$\Leftrightarrow \sqrt{2x+3}-3=2x^2-5x-3$
$\Leftrightarrow \frac{2(x-3)}{\sqrt{2x+3}+3}=(2x+1)(x-3)$
$\Leftrightarrow (x-3)\left[\frac{2}{\sqrt{2x+3}+3}-(2x+1)\right]=0$
Xảy ra 2 TH:
TH1: $x-3=0\Rightarrow x=3$ (thỏa mãn)
TH2: $\frac{2}{\sqrt{2x+3}+3}=2x+1$
Đặt $\sqrt{2x+3}=t(t\geq 0)$ thì pt trở thành: \frac{2}{t+3}=t^2-2$
$\Leftrightarrow 2=(t^2-2)(t+3)\Leftrightarrow t^3+3t^2-2t-8=0$
$\Leftrightarrow (t+2)(t^2+t-4)=0$
Do $t\geq 0$ nên $t=\frac{-1+\sqrt{17}}{2}$
$\Leftrightarrow \sqrt{2x+3}=\frac{-1+\sqrt{17}}{2}\Leftrightarrow x=\frac{3-\sqrt{17}}{4}$ (thỏa mãn)
Vậy........
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Giai phuong trinh
\(\sqrt{x.\left(x-1\right)}+\sqrt{x\left(x+2\right)}=2x\)
x=0
nhanh nhất có thể
X=0
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giai phuong trinh
\(\left(2x-1\right)^2=12\sqrt{x^2-x-2}-1\)
1)7sqrt{3x-7}+left(4x-7right)sqrt{7-x}322)4x^2-11x+6left(x-1right)sqrt{2x^2-6x+6}3)9+3sqrt{xleft(3-2xright)}7sqrt{x}+5sqrt{3-2x}4)sqrt{2x^2+4x+7}x^4+4x^3+3x^2-2x-75)frac{6-2x}{sqrt{5-x}}+frac{6+2x}{sqrt{5+x}}frac{8}{3}6)2left(5x-3right)sqrt{x+1}+left(x+1right)sqrt{3-x}3left(5x+1right)7)sqrt{7x+7}+sqrt{7x-6}+2sqrt{49x^2+7x-42}181-14x
Đọc tiếp
1)\(7\sqrt{3x-7}+\left(4x-7\right)\sqrt{7-x}=32\)
2)\(4x^2-11x+6=\left(x-1\right)\sqrt{2x^2-6x+6}\)
3)\(9+3\sqrt{x\left(3-2x\right)}=7\sqrt{x}+5\sqrt{3-2x}\)
4)\(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
5)\(\frac{6-2x}{\sqrt{5-x}}+\frac{6+2x}{\sqrt{5+x}}=\frac{8}{3}\)
6)\(2\left(5x-3\right)\sqrt{x+1}+\left(x+1\right)\sqrt{3-x}=3\left(5x+1\right)\)
7)\(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-14x\)