Úi tận 50 câu trả lời, có lẽ e không đủ rồi

\(\dfrac{1}{sinx}+\dfrac{1}{sin2x}+\dfrac{1}{sin4x}=0\)

\(\dfrac{1}{sinx}+cotx+\dfrac{1}{sin2x}+cot2x+\dfrac{1}{sin4x}+cot4x=cotx+cot2x+cot4x\)

\(\dfrac{1+cosx}{sinx}+\dfrac{1+cos2x}{sin2x}+\dfrac{1+cos4x}{sin4x}=cotx+cot2x+cot4x\)

\(\dfrac{2cos^2\dfrac{x}{2}}{2sin\dfrac{x}{2}.cos\dfrac{x}{2}}+\dfrac{2cos^2x}{2sinx.cosx}+\dfrac{2cos^22x}{2sin2x.cos2x}=cotx+cot2x+cot4x\)

\(\dfrac{cos\dfrac{x}{2}}{sin\dfrac{x}{2}}+\dfrac{cosx}{sinx}+\dfrac{cos2x}{sin2x}=cotx+cot2x+cot4x\)

\(cot\dfrac{x}{2}+cotx+cot2x=cotx+cot2x+cot4x\)

\(cot\dfrac{x}{2}=cot4x\)

\(\Rightarrow\dfrac{x}{2}=4x+k\text{π}\)

\(\Leftrightarrow x=-\dfrac{k2\text{π}}{7}\)

\(6xy\left(\dfrac{1}{2x^2y}-\dfrac{1}{3x^3y^2}-1\right)\)

\(=\dfrac{3}{x}-\dfrac{2}{x^2y}-6xy\)

\(P.Q=\left(2x-3y\right)\left(2x+3y\right)\)

         \(=4x^2-9y^2\)

a) \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x+3\right)\left(x-1\right)}=-\left(x+3+x-1-6\right)\)\(\left(Đk:x\ge1\right)\)

\(\left(\sqrt{x-1}+\sqrt{x+3}\right)^2+\sqrt{x-1}+\sqrt{x-3}-6=0\)

\(\left(\sqrt{x-1}+\sqrt{x+3}+3\right)\left(\sqrt{x-1}+\sqrt{x+3}-2\right)=0\)

Đến đây em xét các trường hợp rồi bình phương lên là được nha

b) \(\sqrt{3x-2}+\sqrt{x-1}=3x-2+x-1-6+2\sqrt{\left(3x-2\right)\left(x-1\right)}\left(Đk:x\ge1\right)\)

\(\left(\sqrt{3x-2}+\sqrt{x-1}\right)^2-\left(\sqrt{3x-2}+\sqrt{x-1}\right)-6=0\)

\(\left(\sqrt{3x-2}+\sqrt{x-1}-3\right)\left(\sqrt{3x-2}+\sqrt{x-1}+2\right)=0\)

Đến đây em xét các trường hợp rồi bình phương lên là được nha

\(\sqrt{8-a}+\sqrt{5+a}=5\left(Đk:-5\le a\le8\right)\)

\(8-a+5+a+2\sqrt{\left(8-a\right)\left(5+a\right)}=25\)

\(\sqrt{\left(8-a\right)\left(5+a\right)}=6\)

\(a^3+b^3+c^3=\left(a+b+c\right)^3-3\left(a+b\right)\left(b+c\right)\left(c+a\right)\)

Ta có: Với 3 số a,b,c ít nhất có 1 cặp a,b,c cùng chẵn hoặc cùng lẻ

=> \(\left[{}\begin{matrix}a+b⋮2\\b+c⋮2\\c+a⋮2\end{matrix}\right.\)=> \(3\left(a+b\right)\left(b+c\right)\left(c+a\right)⋮6\)

=> \(a^3+b^3+c^3⋮6\)

Để \(A\cap B\ne\varnothing\Leftrightarrow m\ge-2\)

\(=2.\left(\dfrac{4}{3.7}+\dfrac{4}{7.11}+...+\dfrac{4}{35.39}\right)\)

\(=2.\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{35}-\dfrac{1}{39}\right)\)

\(=2\left(\dfrac{1}{3}-\dfrac{1}{39}\right)=\dfrac{8}{13}\)