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a) 3x.3x+2 =81
3x.3x.32 =81
3x.3x.9 =81
3x.3x =81/9
3x.3x =9
31.31 =9
x =1
b)2(x+15)+3(x+25)=2050
2(x+15)+3(x+15+10)=2050
2(x+15)+3(x+15)+3.10=2050
(x+15)(2+5)+30=2050
(x+15)5=2050-30
(x+15)5=2020
x+15=2020/5
x+15=404
x =404-15
x =389
c)2x+2x+1+2x+2+2x+3=960
2x+2x.2+2x.22+2x.23=960
2x(1+2+22+23)=960
2x(1+2+4+8)=960
2x.15=960
2x =960/15
2x =64
26 =64
x =6
bài d làm tương tự c,e làm tương tự a
f)3x.32x+3=729
33x.33=729
33x.27 =729
33x =729/27
33x =27
33.1 =27
x =1
2.
\(\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot15\cdot37\right)\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot5\cdot3\cdot37\right)\\=\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-\left(13\cdot5\right)\cdot\left(3\cdot37\right)\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-65\cdot111\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot0\\ =0\)
a)Đặt \(A=3-3^2+3^3-3^4+...+3^{95}-3^{96}\)
\(3A=3^2-3^3+3^4-3^5+...+3^{96}-3^{97}\)
\(3A+A=\left(3^2-3^3+3^4-3^5+...+3^{96}-3^{97}\right)+\left(3-3^2+3^3-3^4+...+3^{95}-3^{96}\right)\)
\(4A=-3^{97}+3\)
\(A=\frac{-3^{97}+3}{4}\)
b)tương tự như câu a
c)\(\left(100-1^2\right)\left(100-2^2\right)\left(100-3^2\right).....\left(100-99^2\right)\)
\(=\left(10^2-1^2\right)\left(10^2-2^2\right)\left(10^2-3^2\right)....\left(10^2-10^2\right)...\left(10^2-99^2\right)\)
\(=\left(10^2-1^2\right)\left(10^2-2^2\right)\left(10^2-3^2\right)...0...\left(10^2-99^2\right)\)
=0
a) 7(x-5)+14=56
<=>7(x-5)=42
<=>x-5=6
<=>x=11
b)9(x+1)-3=15
<=>9(x+1)=18
<=>x+1=2
<=>x=1
c)12(x+5)-36=48
<=>12(x+5)=84
<=>x+5=7
<=>x=2
d)5(x+14)=145
<=>x+14=29
<=>x=15
Nhiều câu quá >.<
a/ \(2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20.\)
\(2x^2+10x=x^2+6x+9+x^2-2x+1+20.\)
\(10x=4x+30\)
\(6x=30\Rightarrow x=5\)
các câu còn lại tương tự
\(a,2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20\)
\(\Leftrightarrow2x^2+10x=x^2+6x+9+x^2-2x+1+20\)
\(\Leftrightarrow2x^2+10x=2x^2+4x+30\)
\(\Leftrightarrow2x^2+10x-2x^2-4x=30\)
\(\Leftrightarrow6x=30\)
\(\Leftrightarrow x=5\)
Vậy ...........
\(b,\left(2x-2\right)^2=\left(x+1\right)^2+3\left(x-2\right)\left(x+5\right)\)
\(\Leftrightarrow4x^2-8x+4=x^2+2x+1+3x^2+15x-6x-30\)
\(\Leftrightarrow4x^2-8x+4=4x^2+11x-29\)
\(\Leftrightarrow4x^2-8x-4x^2-11x=-29-4\)
\(\Leftrightarrow-19x=-33\)
\(\Leftrightarrow x=\frac{33}{19}\)
Vậy...........
\(c,\left(x-1\right)^2+\left(x+3\right)^2=2\left(x-2\right)\left(x+1\right)+38\)
\(\Leftrightarrow x^2-2x+1+x^2+6x+9=2x^2+2x-4x-4+38\)
\(\Leftrightarrow2x^2+4x+10=2x^2-2x+34\)
\(\Leftrightarrow2x^2+4x-2x^2+2x=34-10\)
\(\Leftrightarrow6x=24\)
\(\Leftrightarrow x=4\)
Vậy.............
\(d,\left(x+2\right)^3-\left(x-2\right)^3=12x\left(x-1\right)-18\)
\(\Leftrightarrow x^3+6x+12x+8-\left(x^3-6x+12x-8\right)=12x^2-12x-8\)
\(\Leftrightarrow x^3+6x+12x+8-x^3+6x-12x+8=12x^2-12x-8\)
\(\Leftrightarrow12x=-24\)
\(\Leftrightarrow x=-2\)
Vậy............
Mấy cái này mũ thấp:
a) 48+288:(x-3)2=50 <=> 288:(x-3)2=2 <=> (x-3)2=144 <=> \(\orbr{\begin{cases}x-3=12\\x-3=-12\end{cases}}\)<=>\(\orbr{\begin{cases}x=9\\x=-15\end{cases}}\).Vậy,...
b) x2-15=1 <=> x=+-4. Vậy,...
c) 45:x=5 <=> x=9. Vậy,...
a,3+2x-1=24-[42-(22-2)]
=>3+2x-1=24-(16-2)
=>3+2x-1=24-14
=>3+2x-1=10
=>2x-1=10-3
=>2x-1=7
=>sai đề
a) x = 17
b) x = 23
c) x = 63
d) x = 2499
e) x = -3
j) x = 3
g) x = 7
h) x = 3
2.x2 = 32
x2 = 9 : 2
x2 = 9/2
x =+ - \(\sqrt{\dfrac{9}{2}}\)
x = + - \(\dfrac{3\sqrt{2}}{2}\)