\(b,\left(x+5\right)^2=100\)

TH1:\(\left(x+5\right)^2=10^2\)

        \(\Rightarrow x+5=10\\ \Rightarrow x=10-5\\ \Rightarrow x=5\)

TH2:\(\left(x+5\right)^2=\left(-10\right)^2\)

         \(\Rightarrow x+5=-10\\ \Rightarrow x=-10-5\\ \Rightarrow x=-15\)

\(c,\left(2x-4\right)^2=0\\ \Rightarrow2x-4=0\\ \Rightarrow2x=0+4\\ \Rightarrow x=2:2\\ \Rightarrow x=1\)

\(d,\left(x-1\right)^3=-27\\ \Rightarrow\left(x-1\right)^3=\left(-3\right)^3\\ \Rightarrow x-1=-3\\ \Rightarrow x=-3+1\\ \Rightarrow x=-2\)

b) (x+5)²=100
    (x+5)²=10²
     x+5=10
     x=10-5
     x=5
c) (2x-4)²=0
    2x-4=0
    2x=4
      x=4:2
      x=\(\pm\)2
d)(x-1)³=-27
   (x-1)³=-3³
    x-1=-3
    x=-3+1
    x=-2

b: \(=\dfrac{x^2-x+1-3+1-x^2}{\left(x+1\right)\cdot\left(x^2-x+1\right)}=\dfrac{-x-1}{\left(x+1\right)\left(x^2-x+1\right)}=\dfrac{-1}{x^2-x+1}\)

a. \(f\left(x\right)_{max}=f\left(-2\right)=111\) ; \(f\left(x\right)_{min}=f\left(1\right)=-6\)

b. \(f\left(x\right)_{max}=f\left(-3\right)=7\) ; \(f\left(x\right)_{min}=f\left(0\right)=1\)

c. \(f\left(x\right)_{max}=f\left(4\right)=\dfrac{2}{3}\) ; \(f\left(x\right)_{min}\) ko tồn tại

d. 

Miền xác định: \(D=\left[-2\sqrt{2};2\sqrt{2}\right]\)

\(y'=\dfrac{2\left(4-x^2\right)}{\sqrt{8-x^2}}=0\Rightarrow\left[{}\begin{matrix}x=-2\\x=2\end{matrix}\right.\)

\(f\left(-2\sqrt{2}\right)=f\left(2\sqrt{2}\right)=0\)

\(f\left(-2\right)=-4\) ; \(f\left(2\right)=4\)

\(f\left(x\right)_{max}=f\left(2\right)=4\) ; \(f\left(x\right)_{min}=f\left(-2\right)=-4\)

`a)P(x)+Q(x)=x^5-2x^2+1`

`=>Q(x)=x^5-2x^2+1-P(x)`

`=>Q(x)=x^5-2x^2+1-x^4+3x^2-1/2+x`

`=>Q(x)=x^5-x^4+x^2+x+1/2`

______________________________________________

`b)P(x)-R(x)=x^3`

`=>R(x)=P(x)-x^3`

`=>R(x)=x^4-3x^2+1/2-x-x^3`

`=>R(x)=x^4-x^3-3x^2-x+1/2`

Ta có:

\(P\left(x\right)+Q\left(x\right)=x^5-2x^2+1\)

\(\Rightarrow Q\left(x\right)=P\left(x\right)-\left(x^5-2x^2+1\right)\)

\(=x^4-3x^2+\dfrac{1}{2}-x-x^5+2x^2-1\)

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

Vậy \(Q\left(x\right)=-5^2+x^4-x^2-x-\dfrac{1}{2}\)

a) <=> Q(x) = (x⁵ - 2x² + 1) - P(x)

= (x⁵ - 2x² + 1) - (x⁴ - 3x² + 1/2 - x)

= x⁵ - 2x² + 1 - x⁴ + 3x² + x - 1/2

= x⁵ - x⁴ + x² + x + 1/2

Vậy Q(x) = x⁵ - x⁴ + x² + x + 1/2

À ý em lộn)):

\(\dfrac{a^3}{b\left(c+2\right)}+\dfrac{b}{3}+\dfrac{c+2}{9}\ge3\sqrt[3]{\dfrac{a^3b\left(b+2\right)}{27b\left(c+2\right)}}=a\)

Tương tự: \(\dfrac{b^3}{c\left(a+2\right)}+\dfrac{c}{3}+\dfrac{a+2}{9}\ge b\)

\(\dfrac{c^3}{a\left(b+2\right)}+\dfrac{a}{3}+\dfrac{b+2}{9}\ge c\)

Cộng vế:

\(VT+\dfrac{4\left(a+b+c\right)}{9}+\dfrac{2}{3}\ge a+b+c\)

\(\Rightarrow VT\ge\dfrac{5\left(a+b+c\right)}{9}-\dfrac{2}{3}\ge\dfrac{15}{9}-\dfrac{2}{3}=1\)

c: Ta có: AM//BC

AE⊥BC

Do đó:AM⊥AE

Suy ra: \(\widehat{AME}+\widehat{AEM}=90^0\)

hay \(\widehat{AME}+\widehat{BAD}=90^0\)