Ta có: \(x^4-30x^2+31x-30=0\) \(\Rightarrow x^4+x-30x^2+30x-30=0\)

\(\Rightarrow x\left(x^3+1\right)-30\left(x^2-x+1\right)=0\)

\(\Rightarrow x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)=0\)

\(\Rightarrow\left(x^2-x+1\right)\left(x^2+x-30\right)=0\)

Xét \(x^2-x+1=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0\)

\(\Rightarrow x^2+x-30=0\Rightarrow x^2-5x+6x-30=0\)

\(\Rightarrow\left(x-5\right)\left(x+6\right)=0\Rightarrow\orbr{\begin{cases}x-5=0\\x+6=0\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=-6\end{cases}}}\)

Vậy x=5 hoặc x = -6

A=\(4+8+12+...+96\)

Số phần tử: \(\dfrac{96-4}{4}+1=24\)

Tổng của A: \(=\left(96+4\right)\cdot\dfrac{24}{2}=1200\)

A=0;4;8;....;96;100

DÃY SỐ TRÊN CÓ LÀ:(100-0):4+1=26(SỐ)

VẬY A GỒM 26 SỐ

Ta có : A={xϵn | x < 100, x chia hết cho 4 }

A= {0,4,8,12,......,92,96}

Số cấc số hạng : (96-0):4+1=24 (số)

Tổng của các STN đó: (96+0)x24:2=1152

mik cần gấp giúp vs ạ

\(\Leftrightarrow x^4-5x^3+5x^3-25x^3-5x^3+25x+6x-30=0\)

\(\Leftrightarrow\left(x-5\right)\left(x^3+5x^2-5x+6\right)=0\)

\(\Leftrightarrow\left(x-5\right)\cdot\left(x^3+6x^2-x^2-6x+x+6\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+6\right)\left(x^2-x+1\right)=0\)

hay \(x\in\left\{5;-6\right\}\)

\(3^2\cdot\left(x+4\right)-5^2=5\cdot22\)

\(\Rightarrow9\cdot\left(x+4\right)-25=110\)

\(\Rightarrow9\cdot\left(x+4\right)=110+25\)

\(\Rightarrow9\cdot\left(x+4\right)=135\)

\(\Rightarrow x+4=\dfrac{135}{9}\)

\(\Rightarrow x+4=15\)

\(\Rightarrow x=15-4\)

\(\Rightarrow x=11\)

`#3107`

\(3^2\cdot\left(x+4\right)-5^2=5\cdot22\\ \Rightarrow3^2\left(x+4\right)=5\cdot22+5^2\\ \Rightarrow9\left(x+4\right)=110+25\\ \Rightarrow9\left(x+4\right)=135\\ \Rightarrow x+4=135\div9\\ \Rightarrow x+4=15\\ \Rightarrow x=15-4\\ \Rightarrow x=11\)

Vậy, `x = 11.`

TA CÓ:

\(\sqrt{x-1-4\sqrt{x-1}+4}+\sqrt{x-1+6\sqrt{x-1}+9}=5\)

\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}-2\right)^2}+\sqrt{\left(\sqrt{x-1}-3\right)^2}=5\)

\(\Leftrightarrow\sqrt{x-1}-2+\sqrt{x-1}-3=5\Leftrightarrow2\sqrt{x-1}=10\Leftrightarrow\sqrt{x-1}=5\)

\(\Leftrightarrow x-1=25\Leftrightarrow x=26\)

ĐKXĐ: \(x\ge1\)

PT (=) \(\sqrt{\left(\sqrt{x-1}-2\right)^2}+\sqrt{\left(\sqrt{x-1}+3\right)^2}=5\) 

     (=) \(\sqrt{x-1}-2+\sqrt{x-1}+3=5\) (=)  \(2\sqrt{x-1}=4\)(=) \(\sqrt{x-1}=2\)(=) X = 5 (nhận)

Bạn trên làm sai rồi mà bạn :))

\(\Leftrightarrow x+y+z-2\sqrt{x}-2\sqrt{y-1}-2\sqrt{z-2}=0\)
\(\Leftrightarrow\left(x-2\sqrt{x}+1\right)+\left(y-1-2\sqrt{y-1}+1\right)+\left(z-2-2\sqrt{z-2}+1\right)=0\)
\(\Leftrightarrow\left(\sqrt{x}-1\right)^2+\left(\sqrt{y-1}-1\right)^2+\left(\sqrt{z-2}-1\right)^2=0\)
\(VT\ge0\)
Dấu "=" xảy ra \(\Leftrightarrow\sqrt{x}=1;\sqrt{y-1}=1;\sqrt{z-2}=1\)
\(\Leftrightarrow x=1;y=2;z=3\)
\(\Rightarrow x^2_0+y^2_0+z^2_0=1^2+2^2+3^2=14\)

\(2^{2x}+2^{2x+1}=48\)

\(2^{2x}+2^{2x}.2=48\)

\(2^{2x}.\left(1+2\right)=48\)

\(2^{2x}.3=48\)

\(2^{2x}=48:3\)

\(2^{2x}=16\)

\(2^{2x}=2^4\)

\(\Rightarrow2x=4\)

\(x=4:2\)

\(x=2\)

\(2^{2x}+2^{2x+1}=48\\ \Rightarrow2^{2x}+2.2^{2x}=48\\ \Rightarrow\left(1+2\right).2^{2x}=48\\ \Leftrightarrow3.2^{2x}=48\\ \Leftrightarrow2^{2x}=16\\ \Leftrightarrow2^{2x}=2^4\\ \Leftrightarrow2x=4\\ \Leftrightarrow x=2\)

Vậy x = 2

x = 2