\(\left|x\right|=\left|y\right|\) và \(x>0;y< 0\)

\(\Rightarrow y=-x\)

\(\Rightarrow2x\pm x=x\)

Vậy \(2x+y=x\)

Ta có:

\(a^2+a+1=\left(a^2+2.a.\dfrac{1}{2}+\dfrac{1}{4}\right)+\dfrac{3}{4}=\left(a+\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\forall a\)

\(\Rightarrow\)PT đã cho vô nghiệm

Vậy không có giá trị \(a\) thỏa mãn \(P=a^{2014}+\dfrac{1}{a^{2014}}\)

11

Ta có:

\(\left|x-\dfrac{1}{3}\right|+\left|x-\dfrac{1}{15}\right|+...+\left|x-\dfrac{1}{399}\right|\ge0\forall x\)

\(\Rightarrow-11x\ge0\forall x\Rightarrow x\le0\)

\(\Rightarrow x-\dfrac{1}{3};x-\dfrac{1}{15};...;x-\dfrac{1}{399}< 0\)

\(\Rightarrow x-\dfrac{1}{3}+x-\dfrac{1}{15}+...+x-\dfrac{1}{399}=11x\)

\(\Rightarrow x+x+...+x-\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{19.21}\right)=11x\)

Vì số lượng \(x\) ở vế trái bằng số lượng số hạng là phân số

\(\Rightarrow\) Số lượng \(x\) ở vế trái là:\(\left(19-1\right):2+1=10\left(số\right)\)

\(\Rightarrow10x-\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{21}\right)=11x\)

\(\Rightarrow-x=1-\dfrac{1}{21}\)

\(\Rightarrow x=-\dfrac{20}{21}\)

\(Ư\left(240\right)=\left\{\text{1;2,3,4,5,6,8,10,24,30,40,48,60,80,120,240}\right\}\)

\(3^{x+1}=27\)

\(\Rightarrow3^{x+1}=3^3\)

\(\Rightarrow x+1=3\)

\(\Rightarrow x=3-1\)

\(\Rightarrow x=2\)

Xem lại đề!

a) \(14\left(x+2\right)=280\)

\(\Rightarrow x+2=280:14\)

\(\Rightarrow x+2=20\)

\(\Rightarrow x=20-2\)

\(\Rightarrow x=18\)

b) \(\left(7x-15\right):2^2-3=2\)

\(\Rightarrow\left(7x-15\right):4-3=2\)

\(\Rightarrow\left(7x-15\right):4=2+3\)

\(\Rightarrow\left(7x+15\right):4=5\)

\(\Rightarrow7x+15=5.4\)

\(\Rightarrow7x+15=20\)

\(\Rightarrow7x=20-15\)

\(\Rightarrow7x=5\)

\(\Rightarrow x=5:7\)

\(\Rightarrow x=\dfrac{5}{7}\)

Mà \(x\inℕ\)

\(\Rightarrow x\in\varnothing\)

a) \(140:\left(x-8\right)=7\)

\(\Rightarrow x-8=140:7\)

\(\Rightarrow x-8=20\)

\(\Rightarrow x=20+8\)

\(\Rightarrow x=28\)

b) \(4\left(x+41\right)=400\)

\(\Rightarrow x+41=400:4\)

\(\Rightarrow x+41=100\)

\(\Rightarrow x=100-41\)

\(\Rightarrow x=59\)

\(M=1+2+2^2+2^3+2^4+...+2^{99}\)

\(\Rightarrow2M=2\left(1+2+2^2+2^3+2^4+...+2^{99}\right)\)

\(\Rightarrow2M=2+2^2+2^3+2^4+2^5+...+2^{100}\)

\(\Rightarrow2M-M=\left(2+2^2+2^3+2^4+2^5+...+2^{100}\right)-\left(1+2+2^2+2^3+2^4+...+2^{99}\right)\)

\(\Rightarrow M=2^{100}-1\)