\(4^{2-x}=4^{16x}\)

\(2-x=16x\)

\(17x=-2\)

\(x=-\dfrac{2}{17}\)

\(9^x=18^4\)

\(3^{2x}=\left(2.9\right)^{2.2}\)

\(3^{2x}=\left(2^2.3^4\right)^2\)

\(3^{2x}=2^4.3^8\)

\(3^{2x}=2^4.3^8\)

\(3^{2x}:3^8=2^4\)

\(3^{2x-8}=2^4\)

Đến đây tôi không biết, mời các bạn giải giúp tiếp, xin cảm ơn

\(S=\dfrac{1}{1.4}+\dfrac{1}{4.7}+...+\dfrac{1}{304.307}\)

\(S=\dfrac{1}{3}\left(1-\dfrac{1}{4}\right)+\dfrac{1}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}\right)+...+\dfrac{1}{3}\left(\dfrac{1}{304}-\dfrac{1}{307}\right)\)

\(S=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...-\dfrac{1}{304}+\dfrac{1}{304}-\dfrac{1}{307}\right)\)

\(S=\dfrac{1}{3}\left(1-\dfrac{1}{307}\right)\)

\(S=\dfrac{1}{3}.\dfrac{306}{307}\)

\(S=\dfrac{102}{307}\)

C) \(\left(x^2-3\right)\left(x^2+3\right)-5x^2\left(x+1\right)^2-\left(x^2-3x\right)\left(x^2-2x\right)+4x\left(x+2\right)^2\)

\(\left(x^4-9\right)-5x^2\left(x^2+2x+1\right)-\left(x^4-2x^3-3x^3+6x^2\right)+4x\left(x^2+4x+4\right)\)

\(x^4-9-5x^4-10x^3-5x^2-x^4+5x^3-6x^2+4x^3+16x^2+16x\)

\(-5x^4-x^3+5x^2+20x-9\)

D) \(-6x^2\left(x+5\right)^2-\left(x-3\right)^2+\left(x^2-2\right)\left(2x^2+1\right)-4x^2\left(3x-4\right)^2\)

\(-6x^2\left(x^2+10x+25\right)-\left(x^2-6x+9\right)+2x^4-3x^2-2-4x^2\left(9x^2-24x+16\right)\)

\(-6x^4-60x^3+150x^2-x^2+6x-9+2x^4-3x^2-2-36x^4+96x^3-64x^2\)

\(-40x^4+36x^3+82x^2+6x-11\)

Chu vi mảnh vườn là :

\(\left(5,5+3,75\right).2=18.5m\)

Số khóm hoa cần trồng là : 

\(18,5:\dfrac{1}{4}=74\left(khóm\right)\)

a) \(\dfrac{1}{5}+\dfrac{4}{5}:x=0\)

  \(\dfrac{4}{5}:x=-\dfrac{1}{5}\)

  \(x=\dfrac{4}{5}:-\dfrac{1}{5}\)

\(x=\dfrac{4}{5}:-\dfrac{1}{5}\)

\(x=-4\)

b) \(x+\dfrac{1}{2}=1-x\)

\(2x=\dfrac{1}{2}\)

\(x=\dfrac{1}{4}\)

a) \(\dfrac{2}{3}.\dfrac{5}{4}-\dfrac{3}{4}.\dfrac{2}{3}\)

= \(\dfrac{5}{6}-\dfrac{1}{2}\)

= \(\dfrac{1}{3}\)

b) \(2.\left(\dfrac{-3}{2}\right)^2-\dfrac{7}{2}\)

= \(2.\dfrac{9}{4}-\dfrac{7}{2}\)

= \(\dfrac{9}{2}-\dfrac{7}{2}\)

= 1

c) \(-\dfrac{3}{4}.5\dfrac{3}{13}-0,75.\dfrac{36}{13}\)

= \(-\dfrac{3}{4}.\dfrac{68}{13}-\dfrac{75}{100}.\dfrac{36}{13}\)

= \(-\dfrac{51}{13}-\dfrac{27}{13}\)

= \(-\dfrac{78}{13}\)

1) ab=2 (I); bc=3 (II); ca=54 (III)

Lấy (I).(II).(III) ⇒ a² . b² . c² = 324 ⇒ abc = ±18

(II) ⇒ a= ±6 ; (I) ⇒ b= ±1/3 ; (II) ⇒ c= ±9

2) ab=5/3 (I); bc=4/5 (II); ca=3/4 (III)

Lấy (I).(II).(III) ⇒ a² . b² . c² = 1 ⇒ abc = ±1

(II) ⇒ a= ±5/4 ; (I) ⇒ b= ±4/3 ; (II) ⇒ c= ±3/5

3) a(a+b+c)= -12 (I)

    b(a+b+c)= 18 (II)

    c(a+b+c)= 30 (III)

Lấy (I)+(II)+(III) ⇒ (a+b+c)² = 36 ⇒ a+b+c = ±6

TH1 : a=6 ⇒ a= -12/6 = -2 ; b= 18/6 = 3 ; c= 30/6 = 5

TH2 : a=-6 ⇒ a= -12/-6 = 2 ; b= 18/-6 = -3 ; c= 30/-6 = -5

27 < 81³ : 3^x <243

⇒ 3³ < (3⁴)³ : 3^x <3⁵

⇒ 3³ < 3¹² : 3^x <3⁵

⇒ 3³ < 3^12-x <3⁵

⇒ 3 <12-x < 5

⇒ -9 < x < 7