K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Các câu hỏi dưới đây có thể giống với câu hỏi trên
28 tháng 8 2017
Ta có \(5^5-5^4+5^3=5^3\left(5^2-5+1\right)=5^3.21=5^3.3.7\)
Vì 53.3 là số nguyên nên \(5^3.3.7⋮7\)
Vậy \(5^5-5^4+5^3⋮7\)
28 tháng 8 2017
c) \(3^{x+3}+3^{x+1}+2^{x+3}+2^{x+2}\)
\(=\left(3^{x+3}+3^{x+1}\right)+\left(2^{x+3}+2^{x+2}\right)\)
\(=3^x\left(3^2+3\right)+2^x\left(2^2+2\right)\)
\(=3^x.12+2^x.6\)
\(=6\left(2.3^x+2^x\right)\)
Vì \(2.3^x+2^x\in Z\)
Nên : \(6\left(2.3^x+2^x\right)⋮6\)
Vậy \(3^{x+3}+3^{x+1}+2^{x+3}+2^{x+2}⋮6\)
29 tháng 8 2017
a) ta có : \(5^5-5^4+5^3=5^3.\left(5^2-5+1\right)=5^3.\left(25-5+1\right)\)
\(5^3.21=5^3.3.7⋮7\) (đpcm)
b) ta có : \(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)=7^4.\left(49+7-1\right)\)
\(=7^4.55=7^4.5.11⋮11\) (đpcm)
c) ta có : \(3^{x+2}-2^{x+3}+3^x-2^{x+1}=3^{x+2}+3^x-2^{x+3}-2^{x+1}\)
\(=3^x\left(3^2+1\right)-2^x\left(2^3+2\right)=3^x.\left(9+1\right)-2^x.\left(8+2\right)\)
\(=3^x.10-2^x.10=10\left(3^x-2^x\right)⋮10\) (đpcm)
d) \(3^{x+3}+3^{x+1}+2^{x+3}+2^{x+2}=3^x.\left(3^3+3\right)+2^x.\left(2^3+2^2\right)\)
\(=3^x.\left(27+3\right)+2^x\left(8+4\right)=3^x.30+2^x.12=6.\left(3^x.5+2^x.2\right)⋮6\) (đpcm)
29 tháng 8 2017
a)Ta có:\(5^5-5^4+5^3=5^3\left(5^2-5+1\right)=5^3.21\)(vì 21 chia hết cho 7)
\(\)\(\RightarrowĐPCM\)
b)Ta có: \(7^6+7^5-7^4⋮11=7^4\left(7^2+7-1\right)=7^4.55⋮11\)
\(\Rightarrowđpcm\)
4 tháng 8 2019
a) \(-12\left(x-5\right)+7\left(3-x\right)=15\)
\(\Leftrightarrow-12x+60+21-7x=15\)
\(\Leftrightarrow-19x=15-\left(60+21\right)=-66\)
\(\Leftrightarrow x=\frac{-66}{-19}=\frac{66}{19}\)
Vậy : \(x=\frac{66}{19}\)
b) \(-\left(2x-3\right)-4\left(x+1\right)=-7x+3\)
\(\Leftrightarrow-2x+3-4x-4=-7x+3\)
\(\Leftrightarrow-2x-4x+7x=3-3+4\)
\(\Leftrightarrow x=4\)
Vậy : \(x=4\)
c) \(-5.\left(x+\frac{1}{5}\right)-\frac{1}{2}.\left(x-\frac{2}{3}\right)=\frac{3}{2}.\frac{-5}{6}\)
\(\Leftrightarrow-5x-1-\frac{1}{2}x+\frac{1}{3}=-\frac{5}{4}\)
\(\Leftrightarrow-\frac{11}{2}x=-\frac{5}{4}+1-\frac{1}{3}=-\frac{7}{12}\)
\(\Leftrightarrow x=-\frac{7}{12}:\frac{-11}{2}=\frac{7}{66}\)
Vậy : \(x=\frac{7}{66}\)
Câu d) Xíu làm mình bận >>
4 tháng 8 2019
d) \(x-\left\{\left[-x+\left(x+3\right)\right]\right\}-\left[\left(x+3\right)-\left(x-2\right)\right]=0\)
\(\Leftrightarrow x-\left[-x+x+3\right]-\left[x+3-x+2\right]=0\)
\(\Leftrightarrow x+x-x-3-x-3+x-2=0\)
\(\Leftrightarrow\left(x+x-x-x+x\right)+\left(-3-3-2\right)=0\)
\(\Leftrightarrow x+\left(-8\right)=0\)
\(\Leftrightarrow x=8\)
Vậy : \(x=8\)
P/s : Câu này cần chú ý quy tắc chuyển dấu và quy tắc thực hiện khi có dấu ngoặc nhé !
31 tháng 5 2022
a: \(\Leftrightarrow\dfrac{7}{2}x-\dfrac{3}{4}=\dfrac{1}{2}x+\dfrac{5}{2}\)
\(\Leftrightarrow3x=\dfrac{5}{2}+\dfrac{3}{4}=\dfrac{10}{4}+\dfrac{3}{4}=\dfrac{13}{4}\)
=>x=13/12
b: \(\Leftrightarrow x\cdot\left(\dfrac{2}{3}-\dfrac{1}{2}\right)=-\dfrac{1}{3}+\dfrac{2}{5}\)
\(\Leftrightarrow x\cdot\dfrac{1}{6}=\dfrac{-5+6}{15}=\dfrac{1}{15}\)
\(\Leftrightarrow x=\dfrac{1}{15}:\dfrac{1}{6}=\dfrac{2}{5}\)
c: \(\Leftrightarrow x\cdot\dfrac{1}{3}+x\cdot\dfrac{2}{5}+\dfrac{2}{5}=0\)
\(\Leftrightarrow x\cdot\dfrac{11}{15}=-\dfrac{2}{5}\)
\(\Leftrightarrow x=-\dfrac{2}{5}:\dfrac{11}{15}=\dfrac{-2}{5}\cdot\dfrac{15}{11}=\dfrac{-30}{55}=\dfrac{-6}{11}\)
d: \(\Leftrightarrow-\dfrac{1}{3}x+\dfrac{1}{2}+\dfrac{2}{3}-x-\dfrac{1}{2}=5\)
\(\Leftrightarrow-\dfrac{4}{3}x+\dfrac{2}{3}=5\)
\(\Leftrightarrow-\dfrac{4}{3}x=5-\dfrac{2}{3}=\dfrac{13}{3}\)
\(\Leftrightarrow x=\dfrac{13}{3}:\dfrac{-4}{3}=\dfrac{-13}{4}\)
e: \(\Leftrightarrow\left(\dfrac{x+2015}{5}+1\right)+\left(\dfrac{x+2016}{4}+1\right)=\left(\dfrac{x+2017}{3}+1\right)+\left(\dfrac{x+2018}{2}+1\right)\)
=>x+2020=0
hay x=-2020
VM
26 tháng 7 2019
Bài 1:
a) \(\frac{1}{5}x^4y^3-3x^4y^3\)
= \(\left(\frac{1}{5}-3\right)x^4y^3\)
= \(-\frac{14}{5}x^4y^3.\)
b) \(5x^2y^5-\frac{1}{4}x^2y^5\)
= \(\left(5-\frac{1}{4}\right)x^2y^5\)
= \(\frac{19}{4}x^2y^5.\)
Mình chỉ làm 2 câu thôi nhé, bạn đăng nhiều quá.
Chúc bạn học tốt!
Sure, let's solve the equation step by step:
Given Equation:
2⋅3x−1+5⋅3x−3=18632⋅3x−1+5⋅3x−3=1863Step 1: Combine Like Terms
First, combine the terms with 3x3x and the constant terms separately:
(2⋅3x+5⋅3x)+(−1−3)=1863(2⋅3x+5⋅3x)+(−1−3)=1863 7⋅3x−4=18637⋅3x−4=1863Step 2: Isolate the Exponential Term
Add 4 to both sides of the equation to isolate the term with 3x3x:
7⋅3x=1863+47⋅3x=1863+4 7⋅3x=18677⋅3x=1867Step 3: Solve for 3x3x
Divide both sides by 7 to solve for 3x3x:
3x=186773x=71867 3x=266.7142857(approximately)3x=266.7142857(approximately)Step 4: Solve for xx Using Logarithms
To solve for xx, take the logarithm base 3 of both sides:
x=log3(18677)x=log3(71867)Using the change of base formula or a calculator:
x=ln(18677)ln(3)≈ln(266.7142857)ln(3)≈5.8891.0986≈5.36x=ln(3)ln(71867)≈ln(3)ln(266.7142857)≈1.09865.889≈5.36Final Answer:
x≈5.36x≈5.36\(2\cdot3^{x-1}+5\cdot3^{x-3}=1863\)
=>\(2\cdot3^x\cdot\dfrac{1}{3}+5\cdot3^x\cdot\dfrac{1}{27}=1863\)
=>\(3^x\left(\dfrac{2}{3}+\dfrac{5}{27}\right)=1863\)
=>\(3^x\cdot\dfrac{23}{27}=1863\)
=>\(3^x=1863:\dfrac{23}{27}=2187=3^7\)
=>x=7