\(\sqrt{\frac{y+1}{\left(x+2\right)^2}}.\sqrt{\frac{\left(x-2\right)^6}{y^2-2y+1}}\)

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

\(=\frac{\sqrt{y+1}}{x+2}.\frac{\left(x-2\right)^6}{y-1}\)

\(=\frac{-\left(x-2\right)^5\sqrt{y+1}}{y-1}\)

a: \(A\left(\dfrac{1}{2}\right)=-2\cdot\dfrac{1}{8}+3\cdot\dfrac{1}{4}+5=\dfrac{11}{2}\)

\(A\left(1\right)=-2+3+5=6\)

\(A\left(-1\right)=2+3+5=10\)

\(A\left(0\right)=-2\cdot0+3\cdot0+5=5\)

\(A\left(-3\right)=-2\cdot\left(-27\right)+3\cdot9+5=86\)

b: Khi x=2 và y=1 thì 

\(B=-3\cdot8\cdot1+2\cdot4-2\cdot2=-20\)

Khi x=-2 và y=1 thì

\(B=-3\cdot\left(-8\right)\cdot1+2\cdot4-2\cdot\left(-2\right)=36\)

\(=4.\left(-\dfrac{1}{8}\right)-2.\dfrac{1}{4}-\dfrac{3}{2}+1=\)

\(=-\dfrac{1}{2}-\dfrac{1}{2}-\dfrac{3}{2}+1=-\dfrac{3}{2}\)

= 4 . -1/8 - 2 . -1/4 + 3 . -1/2 + 1

= -1/2 - -1/2 + -3/2 + 1

= -1/2

cảm ơn nhìu

Đề có vẻ thiếu điều kiện để tìm min. Bạn xem lại.

Công thức tổng quát:

\(1-\frac{1}{n^2}=\left(\frac{n-1}{n}\right)\left(\frac{n+1}{n}\right)\)

Do đó:

\(A=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{12^2}\right)\)

\(A=\frac{1}{2}.\frac{3}{2}.\frac{2}{3}.\frac{4}{3}.\frac{3}{4}.\frac{5}{4}....\frac{11}{12}.\frac{13}{12}\)

\(A=\frac{1}{2}.\frac{13}{12}=\frac{13}{24}\)

tk mk , mk tk 

\(\sqrt{\left(\sqrt{3}+1\right)^2}+\sqrt{\left(1-\sqrt{3}\right)^2}\)

\(=\sqrt{3}+1+\sqrt{3}-1\)

\(=2\sqrt{3}\)

mũ 2 với căn lớn bên ngoài sẽ triệt tiêu cho nhau
=\(\sqrt{3}+1+1-\sqrt{3}=2\)

Tính:

b) \(\left(-2\right)^3.\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)

\(=\left(-2\right)^3.\left(\frac{3}{4}-\frac{1}{4}\right):\left(\frac{9}{4}-\frac{7}{6}\right)\)

\(=\left(-8\right).\frac{1}{2}:\frac{13}{12}\)

\(=\left(-4\right):\frac{13}{12}\)

\(=-\frac{48}{13}.\)

Tìm x

a) \(4\frac{1}{3}:\frac{x}{4}=6:0,3\)

⇒ \(\frac{13}{3}:\frac{x}{4}=20\)

⇒ \(\frac{x}{4}=\frac{13}{3}:20\)

⇒ \(\frac{x}{4}=\frac{13}{60}\)

⇒ \(x.60=4.13\)

⇒ \(x.60=52\)

⇒ \(x=52:60\)

⇒ \(x=\frac{13}{15}\)

Vậy \(x=\frac{13}{15}.\)

b) \(\left(2^3:4\right).2^{x+1}=64\)

⇒ \(\left(8:4\right).2^{x+1}=64\)

⇒ \(2.2^{x+1}=64\)

⇒ \(2^{x+1}=64:2\)

⇒ \(2^{x+1}=32\)

⇒ \(2^{x+1}=2^5\)

⇒ \(x+1=5\)

⇒ \(x=5-1\)

⇒ \(x=4\)

Vậy \(x=4.\)

Chúc bạn học tốt!