không có j nha

\(P=\dfrac{\sqrt{x}\left(\sqrt{x}+2+\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{x-4}{\sqrt{4x}}\)\(\left(x\ge0,x\ne4\right)\)

\(=\dfrac{\sqrt{4x^2}}{x-4}.\dfrac{x-4}{\sqrt{4x}}=\sqrt{x}\)

\(P>3\Leftrightarrow\sqrt{x}>3\Rightarrow x>9\)

\(\dfrac{\sqrt{12,1}}{22,5}=\sqrt{\dfrac{12,1}{22,5^2}}=\sqrt{\dfrac{\dfrac{121}{10}}{\dfrac{2025}{4}}}=\sqrt{\dfrac{242}{10125}}\)

\(\dfrac{\sqrt{12^3}}{\sqrt{3^3}.2^2}=\sqrt{\dfrac{12^3}{3^3.4^2}}=\sqrt{\dfrac{3^3.4^3}{3^3.4^2}}=\sqrt{4}=2\)

\(\left(1-\dfrac{2}{2.3}\right)\left(1-\dfrac{2}{3.4}\right)...\left(1-\dfrac{2}{99.100}\right)\)

\(=\left(\dfrac{2.3}{2.3}-\dfrac{2}{2.3}\right)\left(\dfrac{3.4}{3.4}-\dfrac{2}{3.4}\right)...\left(\dfrac{99.100}{99.100}-\dfrac{2}{99.100}\right)\)

\(=\dfrac{4}{2.3}.\dfrac{10}{3.4}...\dfrac{9898}{99.100}\)

\(=\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}...\dfrac{98.101}{99.100}\)

\(=\dfrac{1.2...98}{2.3...99}.\dfrac{4.5...101}{3.4...100}=\dfrac{1}{99}.\dfrac{101}{3}=\dfrac{101}{297}\)

\(4x^2-\dfrac{4}{5}x+1=25\)

\(\left(2x\right)^2-2.2x.\dfrac{1}{5}+\dfrac{1}{25}=25-\dfrac{24}{25}\)

\(\left(2x-\dfrac{1}{5}\right)^2=\left(\dfrac{\sqrt{601}}{5}\right)^2\)

Chia 2 t/h tìm x

\(y=-0,4x\)

\(x=10z\)

\(\Rightarrow y=-4z\)

\(\Rightarrow\) y tỉ lệ thuận với z theo hệ số -4

\(\Rightarrow\) z tỉ lệ thuận với y theo hệ số \(-\dfrac{1}{4}\)

\(a^2+b^2>\left(a-b\right)^2=a^2+b^2-2ab\left(vớia\in N^{\cdot},b\in N^{\cdot}\right)\)

\(A=x^2-x+3=\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{11}{4}\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\forall x\left(vì\left(x-\dfrac{1}{2}\right)^2\ge0\forall x\right)\)

\(MinA=\dfrac{11}{4}\Leftrightarrow x=\dfrac{1}{2}\)

\(B=2x^2-3x+10=2\left(x^2-\dfrac{3}{2}x\right)+10\)

\(=2\left(x^2-\dfrac{3}{2}x+\dfrac{9}{16}\right)+\dfrac{71}{8}\)

\(=2\left(x-\dfrac{3}{4}\right)^2+\dfrac{71}{8}\ge\dfrac{71}{8}\forall x\left(vì\left(x-\dfrac{3}{4}\right)^2\ge0\forall x\right)\)

\(MinB=\dfrac{71}{8}\Leftrightarrow x=\dfrac{3}{4}\)