\(x^2-x=x\left(x-1\right)\)

Câu E bạn xem lại đề nha

F=\(-y^2+2y-6\)

\(=-\left(y^2-2y+6\right)\)

\(=-\left(y-1\right)^2-5\)

Vì \(-\left(y-1\right)^2\le0\forall y\)

\(\Rightarrow F\le-5\forall y\)

\(MaxF=-5\Leftrightarrow y=1\)

Ta có:

\(\widehat{AOC}+\widehat{BOD}=98^o+74^o\)

\(\widehat{AOD}+2\widehat{COD}+\widehat{BOC}=172^o\)

\(\widehat{COD}+\widehat{AOB}=172^o\)

\(\widehat{COD}=172^o-\widehat{AOB}=172^o-136^o=36^o\)

\(\dfrac{3}{17}A=\dfrac{6}{7.13}+\dfrac{9}{13.22}+\dfrac{15}{22.37}+\dfrac{12}{37.49}\)

\(\dfrac{3}{17}A=\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{22}+\dfrac{1}{22}-\dfrac{1}{37}+\dfrac{1}{37}-\dfrac{1}{49}\)

\(\dfrac{3}{17}A=\dfrac{1}{7}-\dfrac{1}{49}=\dfrac{6}{49}\)

\(A=\dfrac{6}{49}:\dfrac{3}{17}=\dfrac{6.17}{49.3}=\dfrac{34}{49}\)

\(313^5.299-313^6.36\)

\(=313^5.299-313^636\)

\(=313^5\left(299-313.36\right)\)

Ta có:

Ta có: \(299\equiv5\left(mod7\right)\)

       \(313\equiv5\left(mod7\right)\)

       \(36\equiv1\left(mod7\right)\)

=> \(299-313.36\equiv5-5.1=0\left(mod7\right)\)

=> \(299-313.36⋮7\)

=> \(313^5.299-313^6.36⋮7\)

\(3^{n+1}-2.3^n+2^{n+5}-7.2^n\)

\(=3^n\left(3-2\right)+2^n\left(2^5-7\right)\)

\(=3^n+2^n.25\)

Vì \(3^n⋮̸25\); \(25.2^n⋮25\)

=> \(3^n+2^n.25⋮̸25\)

=> \(3^{n+1}-2.3^n+2^{n+5}-7.2^n⋮̸25\)

\(A=-\dfrac{1}{3}+\dfrac{1}{3^2}-...-\dfrac{1}{3^{99}}+\dfrac{1}{3^{100}}\)

\(=\dfrac{1}{3}\left(-1+\dfrac{1}{3}\right)+\dfrac{1}{3^3}\left(-1+\dfrac{1}{3}\right)+...+\dfrac{1}{3^{99}}\left(-1+\dfrac{1}{3}\right)\)

\(=\dfrac{-2}{3}\left(\dfrac{1}{3}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)\)

Ta có:

\(B=\dfrac{1}{3}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\)

\(9B=3+\dfrac{1}{3}+...+\dfrac{1}{3^{97}}\)

\(9B-B=3-\dfrac{1}{3^{99}}\)

\(B=\dfrac{3-\dfrac{1}{3^{99}}}{8}\)

\(A=-\dfrac{2}{3}B=\dfrac{-2}{3}.\dfrac{3-\dfrac{1}{99}}{8}=\dfrac{\dfrac{1}{3^{100}}-1}{4}\)

Ta có:

\(x+y=1\Rightarrow3xy=3xy\left(x+y\right)\)

\(x^3+3xy+y^3\)

\(=x^3+3xy\left(x+y\right)+y^3\)

\(=\left(x+y\right)^3=1\)

a) \(2^{x+1}+2^x=3.32\)

\(2^x\left(2+1\right)=3.32\)

\(2^x=32=2^5\)

\(x=5\)

b) \(5^{2x+1}-5^{2x}=100\)

\(5^{2x}\left(5-1\right)=4.25\)

\(5^{2x}=25=5^2\)

x=1

c) \(7^{3x+1}+7^{3x}=343.14^3\)

\(7^{3x}\left(7+1\right)=343.14^3\)

\(7^{3x}=\dfrac{7^3.14^3}{2^3}=7^3.7^3=7^6\)

\(3x=6\)

\(x=2\)