a) \(3119\cdot121-3119\cdot11\cdot11\)

\(=3119\cdot121-3119\cdot\left(11\cdot11\right)\)

\(=3119\cdot121-3119\cdot121\)

\(=3119\left(121-121\right)\)

\(=0\)

b) \(24\cdot\left(123\cdot87\right)+\left(87\cdot123\right)\cdot76\)

\(=\left(123\cdot87\right)\cdot\left(76+24\right)\)

\(=\left(123\cdot87\right)\cdot100\)

\(=1070100\)

\(13^4\cdot16^2=13\cdot13\cdot13\cdot13\cdot16\cdot16\)

\(=13\cdot13\cdot13\cdot13\cdot4\cdot4\cdot4\cdot4\)

\(=\left(13\cdot4\right)\left(13\cdot4\right)\left(13\cdot4\right)\left(13\cdot4\right)\)

\(=52\cdot52\cdot52\cdot52\)

\(=52^4\)

k nha

Vẫn có nha em.

\(\left(x+1\right)^2=25\)

\(\Rightarrow\left(x+1\right)^2=\left(\pm5\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}x+1=5\\x+1=-5\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=5-1\\x=-5-1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=-6\end{matrix}\right.\)

\(\left(x+1\right)\cdot2=25\)

\(2x+2=25\)

\(2x=25-2=23\)

\(x=23:2=11,5\)

`#3107`

\(3^{8x+4}=81^{x+3}\\ \Rightarrow3^{8x+4}=\left(3^4\right)^{x+3}\\ \Rightarrow3^{8x+4}=3^{4x+12}\\ \Rightarrow8x+4=4x+12\\ \Rightarrow8x-4x=12-4\\ \Rightarrow4x=8\\ \Rightarrow x=8\div4\\ \Rightarrow x=2\\ \text{Vậy, x = 2.}\)

Lời giải:

$3^{8x+4}=81^{x+3}$

$3^{8x+4}=(3^4)^{x+3}$

$3^{8x+4}=3^{4(x+3)}$

$\Rightarrow 8x+4=4(x+3)$
$\Rightarrow 2x+1=x+3$

$\Rightarrow x=2$

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

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

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

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

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

\(\Rightarrow x+4=15\)

\(\Rightarrow x=15-4\)

\(\Rightarrow x=11\)

`#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.`

a) Tập hợp A là:

\(A=\left\{16;17;18;19;...;87;88;89\right\}\) 

b) Số lượng số hạng ở tập hợp A:

\(\left(89-16\right):1+1=74\) (số hạng)

Tổng của tập hợp A:
\(\left(89+16\right)\cdot74:2=3885\)

Lời giải:
$(x+2)+(x+4)+(x+6)+....+(x+200)=250$

$(x+x+....+x)+(2+4+6+...+200)=250$

Số lần xuất hiện của x: $(200-2):2+1=100$ (lần)

Suy ra: $100x+(2+4+6+...+200)=250$

$100x+\frac{(200+2).100}{2}=250$

$100x+10100=250$

$100x=-9850$

$x=-98,5$

\(8x+34=150\)

\(\Rightarrow8x=150-34\)

\(\Rightarrow8x=116\)

\(\Rightarrow x=\dfrac{116}{8}\)

\(\Rightarrow x=\dfrac{29}{2}\)

\(8x+34=150\\ \Rightarrow8x=116\\ \Rightarrow x=12.\)

\(64\cdot4^x=16^8\)

\(\Rightarrow4^3\cdot4^x=\left(4^2\right)^8\)

\(\Rightarrow4^{x+3}=4^{16}\)

\(\Rightarrow x+3=16\)

\(\Rightarrow x=16-3\)

\(\Rightarrow x=13\)

Vậy : x=13