\(52^n+33=\left(52^n-1\right)+34\)

\(=\left(52-1\right)\times\left(52^{n-1}+52^{n-2}\times1+...+52\times1^{n-2}+b^{n-1}\right)+17\times2\)

\(=51\times\left(52^{n-1}+52^{n-2}\times1+...+52\times1^{n-2}+1^{n-1}\right)+17\times2\)

\(=17\times3\times\left(52^{n-1}+52^{n-2}\times1+...+52\times1^{n-2}+1^{n-1}\right)+17\times2⋮17\)

\(\Rightarrow52^n+33⋮17\left(ĐPCM\right)\)

Học tốt

\(\sqrt{1-x}+\sqrt{x+4}=3\)

\(\Leftrightarrow5+2\sqrt{\left(1-x\right)\left(x+4\right)}=9\)

\(\Leftrightarrow2\sqrt{\left(1-x\right)\left(x+4\right)}=9-5\)

\(\Leftrightarrow2\sqrt{\left(1-x\right)\left(x+4\right)}=4\)

Bình phương hai vế lên, ta có: (tự làm tiếp, đến đây là dễ rồi)

ĐK: \(x\ge\frac{1}{3}\)

Đặt: \(\sqrt{3x-1}=t\left(t\ge0\right)\)

Ta có pt: \(x^2-x-t^2+t=0\)

<=> \(\left(x^2-t^2\right)-\left(x-t\right)=0\)

<=> \(\left(x-t\right)\left(x+t-1\right)=0\)

<=> \(\Leftrightarrow\orbr{\begin{cases}t=x\\t=1-x\end{cases}}\Leftrightarrow\orbr{\begin{cases}\sqrt{3x-1}=x\\\sqrt{3x-1}=1-x\end{cases}}\)

Em làm tiếp nhé!

 a,

\(ĐKXĐ:x\ge\frac{1}{2}\)

Ta có: \(\sqrt{2x-1}+2=x\)

\(\Rightarrow\sqrt{2x-1}=x-2\)

\(\Rightarrow2x-1=x^2-4x+4\)

\(\Rightarrow6x-x^2-5=0\)

\(\Rightarrow x^2-6x+5=0\)

\(\Rightarrow\left(x-3\right)^2=4\)

\(\Rightarrow\orbr{\begin{cases}x-3=2\\x-3=-2\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=1\end{cases}}}\)

Ban Nguyen Van Tuan Anh phai danh gia 2 ve phuong trinh roi moi duoc binh phuong 2 ve len chu

Tuc la them dieu kien \(\sqrt{2x-1}=x-2\)

                                 <=>\(\hept{\begin{cases}x\ge2\\2x-1=x^2-4x+4\end{cases}}\)

T u do ta moi loai duoc TH x=1 khong thoa man roi moi ket luan PT co nghiem duy nhat x=5

Tu ke \(AH\perp BC\) Dat BH la x >0 

thi Xet tam giac AHB vuong tai H co

AH=\(\sqrt{2-x^2}\) cm   (DL PYTAGO)

=> CH = \(1+\sqrt{3}-x\) cm

Xet tam giac AHC vuong tai H co

\(AC^2=AH^2+HC^2\) Dinh Ly Pytago

<=> \(4=2-x^2+\left(1+\sqrt{3}-x\right)^2\)  

<=> \(4=2-x^2+1+3+x^2+2\sqrt{3}-2x-2\sqrt{3}x\)

<=> \(2\sqrt{3}-2\sqrt{3}x-2x+2=0\) 

<=> \(2\sqrt{3}\left(1-x\right)-2\left(1-x\right)=0\)

<=>\(\left(2\sqrt{3}-1\right)\left(1-x\right)=0\)

<=> x=1 

Suy ra \(AH=\sqrt{2-1}=1\)

cos B =\(\frac{BH}{AB}=\frac{1}{\sqrt{2}}\) => \(\widehat{B}=45^o\)

cos C=\(\frac{HC}{AC}=\frac{1+\sqrt{3}-1}{2}=\frac{\sqrt{3}}{2}=>\widehat{C}=30^o\)

Suy ra \(\widehat{A}=180^o-45^o-30^0=105^0\)

Study well