Giúp mik làm bài 2 với
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Đồ ngu đồ ăn hại cút mịa mài đê :D
a) Ta có: \(\left(2x+7\right)^2=\left(x+3\right)^2\)
\(\Leftrightarrow\left(2x+7\right)^2-\left(x+3\right)^2=0\)
\(\Leftrightarrow\left(2x+7-x-3\right)\left(2x+7+x+3\right)=0\)
\(\Leftrightarrow\left(x+4\right)\cdot\left(3x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\3x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\3x=-10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-\dfrac{10}{3}\end{matrix}\right.\)
Vậy: \(S=\left\{-4;-\dfrac{10}{3}\right\}\)
b) Ta có: \(\left(4x+14\right)^2=\left(7x+2\right)^2\)
\(\Leftrightarrow\left(4x+14\right)^2-\left(7x+2\right)^2=0\)
\(\Leftrightarrow\left(4x+14-7x-2\right)\left(4x+14+7x+2\right)=0\)
\(\Leftrightarrow\left(-3x+12\right)\left(11x+16\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-3x+12=0\\11x+16=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-3x=-12\\11x=-16\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{16}{11}\end{matrix}\right.\)Vậy: \(S=\left\{4;-\dfrac{16}{11}\right\}\)
(2x+7)2=(x+3)2
=>(2x+7)2-(x+3)2=0
=>(2x+7-x-3)(2x+7+x+3)=0
=>(x-4)(3x+10)=0
=>x-4=0 hoặc 3x+10=0
TH1:x-4=0=>x=4
TH2:3x+10=0=>x=-10/3
(4x+14)2=(7x+2)2
(4x+14)2-(7x+2)2=0
(4x+14-7x-2)(4x+14+7x+2)=0
(-3x+12)(11x+16)=0
TH1:-3x+12=0=>x=4
TH2:11x+16=0=>x=-16/11
\(\sqrt{x^2-2x+4}+\sqrt{x^2+5}=9-2x\left(đk:x\le\dfrac{9}{2}\right)\)
\(\Leftrightarrow x^2-2x+4+x^2+5+2\sqrt{\left(x^2-2x+4\right)\left(x^2+5\right)}=81-36x+4x^2\)
\(\Leftrightarrow2\sqrt{\left(x^2-2x+4\right)\left(x^2+5\right)}=2x^2-34x+72\)
\(\Leftrightarrow4\left(x^2-2x+4\right)\left(x^2+5\right)=4x^4+1156x^2+5184-136x^3+288x^2-4896x\)
\(\Leftrightarrow4x^4-8x^3+36x^2-40x+80=4x^4-136x^3+1444x^2-4896x+5184\)
\(\Leftrightarrow128x^3-1408x^2+4856x-5104=0\)
\(\Leftrightarrow128x^2\left(x-2\right)-1152x\left(x-2\right)+2552\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(128x^2-1152x+2552\right)=0\)
\(\Leftrightarrow x=2\left(tm\right)\)(do \(128x^2-1152x+2552>0\))
Do \(\left|x\right|,\left|x^2+x\right|\ge0\forall x\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x^2+x=0\end{matrix}\right.\)
\(\Rightarrow x=0\)
\(A=2+2^2+...+2^{200}\)
\(2A=2^2+2^3+...+2^{200}+2^{201}\)
\(\Rightarrow2A-A=2^{201}-2\)
\(\Rightarrow A=2^{201}-2\)
a: Xét ΔABE và ΔHBE có
BA=BH
\(\widehat{ABE}=\widehat{HBE}\)
BE chung
Do đó: ΔABE=ΔHBE
b: Ta có: ΔABE=ΔHBE
nên \(\widehat{BAE}=\widehat{BHE}=90^0\)
hay HE\(\perp\)BC