Ta có: \(\left(x+2\right)^4+\left(x+4\right)^4\)

\(=\left(x^2+4x+4\right)^2+\left(x^2+8x+16\right)^2\)

\(=x^4+16x^2+16+8x^3+8x^2+32x+x^4+64x^2+256+16x^3+32x^2+256x\)

\(=2x^4+24x^3+120x^2+288x+272\)

Áp dụng t/c dãy tỉ số bằng nhau:

a.

\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{2x}{6}=\dfrac{4y}{20}=\dfrac{2x+4y}{6+20}=\dfrac{28}{26}=\dfrac{14}{13}\)

\(\Rightarrow\left\{{}\begin{matrix}x=3.\dfrac{14}{13}=\dfrac{52}{13}\\y=5.\dfrac{14}{13}=\dfrac{70}{13}\end{matrix}\right.\)

(Em có nhầm đề 26 thành 28 ko nhỉ, số xấu quá)

b.

\(4x=5y\Rightarrow\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{3x}{15}=\dfrac{-2y}{-8}=\dfrac{3x-2y}{15-8}=\dfrac{35}{7}=5\)

\(\Rightarrow\left\{{}\begin{matrix}x=5.5=25\\y=4.2=20\end{matrix}\right.\)

c.

\(\dfrac{x}{-3}=\dfrac{y}{-7}=\dfrac{2x}{-6}=\dfrac{4y}{-28}=\dfrac{2x+4y}{-6-28}=\dfrac{68}{-34}=-2\)

\(\Rightarrow\left\{{}\begin{matrix}x=-3.\left(-2\right)=6\\y=-7.\left(-2\right)=14\end{matrix}\right.\)

d.

\(\dfrac{x}{2}=\dfrac{y}{-3}=\dfrac{z}{4}=\dfrac{4x}{8}=\dfrac{-3y}{9}=\dfrac{-2z}{-8}=\dfrac{4x-3y-2z}{8+9-8}=\dfrac{16}{9}\)

\(\Rightarrow\left\{{}\begin{matrix}x=2.\dfrac{16}{9}=\dfrac{32}{9}\\y=-3.\dfrac{16}{9}=-\dfrac{48}{9}\\z=4.\dfrac{16}{9}=\dfrac{64}{9}\end{matrix}\right.\)

\(\frac{x}{3}\)=\(\frac{5}{6}\)-\(\frac{1}{3}\)<=>\(\frac{x}{3}\)=\(\frac{1}{2}\)<=>x=\(\frac{3}{2}\)

`2^(x-1)=16`

`=> 2^(x-1)=2^4`

`=>x-1=4`

`=> x=4+1`

`=>x=5`

2^{x-1 =} 16

2^x-1 = 2⁴

x - 1 = 4

x      = 4 + 1

x      = 5

\(-\dfrac{2}{3}=\dfrac{x}{-6}\Rightarrow x=\left(-\dfrac{2}{3}\right)\left(-6\right)=4\)

\(-\dfrac{2}{3}=\dfrac{10}{-y}\Rightarrow y=\left(-10\right):\left(-\dfrac{2}{3}\right)=15\)

\(-\dfrac{2}{3}=\dfrac{z}{9}\Rightarrow z=\left(-\dfrac{2}{3}\right).9=-6\)

\(\dfrac{-2}{3}=\dfrac{x}{-6}=\dfrac{10}{-y}=\dfrac{z}{9}\)

\(x=\left(-6.-2\right):3=4;y=\left(-6.10\right):-4=15;z=\left(10.9\right):-15=-6\)

X-1/4.x=6/11.(6/12+9/12+-4/12)

X-1/4.x=6/11.11/12

X-1/4.x=1/2

X.(1-1/4)=1/2

X.(4/4+-1/4)=1/2

X.3/4=1/2

X=1/2:3/4

X=1/2.4/3

X=2/3

Giai thich trong mot bai toan neu co hai dau x ta se ko tinh duoc trong bai toan nay x-25℅.x=6/11.(1/2+3/4+1/3) co hai dau x nen ta phai dua x ra ngoai lam h chung x dung mot minh se la x.1 khi ta bo x ra ngoai thi ben trong con 1-25℅ roi ta tinh ra sau do lam binh thuong