a: \(12+8\cdot\left(\frac14\right)^3+\left\lbrack\left(\frac{1}{2018}\right)^0:\frac12\right\rbrack^2\)

\(=12+8\cdot\frac{1}{64}+\left(1\cdot2\right)^2\)

\(=12+\frac18+4=16+\frac18=16,125\)

b: \(\frac{20^3\cdot\left(-49\right)^2}{14^3\cdot5^4}=\frac{5^3\cdot2^6\cdot7^4}{7^3\cdot2^3\cdot5^4}=\frac{7\cdot2^3}{5}=\frac{7\cdot8}{5}=\frac{56}{5}\)

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{5}=\dfrac{y}{2}=\dfrac{z}{2}=\dfrac{2x+3y+4z}{2\cdot5+3\cdot2+4\cdot2}=\dfrac{54}{24}=\dfrac{9}{4}\)

Do đó: \(\left\{{}\begin{matrix}x=\dfrac{45}{4}\\y=\dfrac{9}{2}\\z=\dfrac{9}{2}\end{matrix}\right.\)

a: =(x^3-8y^3)-(x-2y)

=(x-2y)(x^2+2xy+4y^2)-(x-2y)

=(x-2y)(x^2+2xy+4y^2-1)

b: =2(x^3-4x^2-12x+27)

=2[(x+3)(x^2-3x+9)-4x(x+3)]

=2(x+3)(x^2-7x+9)

cảm ơn nhiều

Ta có: \(4.3^{x+2}-2.3^{x+1}=810\)

\(4.3^{x+1}.3-2.3^{x+1}=810\)

\(2.3^{x+1}\left(2.3-1\right)=810\)

\(2.3^{x+1}.5=810\)

\(3^{x+1}=81=3^4\)

x+1=4

x=3

B

B

\(3^x+2.3^{x-2}=297\)

\(\Rightarrow3^x\left(1+2.3^{-2}\right)=297\)

\(\Rightarrow3^x\left(1+2.\dfrac{1}{3^2}\right)=297\)

\(\Rightarrow3^x\left(1+\dfrac{2}{9}\right)=297\)

\(\Rightarrow3^x\left(\dfrac{9}{9}+\dfrac{2}{9}\right)=297\)

\(\Rightarrow3^x.\dfrac{11}{9}=297\)

\(\Rightarrow3^x=297:\dfrac{11}{9}=297.\dfrac{9}{11}=243\)

\(\Rightarrow3^x=3^5\)

\(\Rightarrow x=5\) (thỏa mãn)

\(3^x+2.3^{x-2}=297\)

\(3^x+2.3^x:3^2=297\)

\(3^x\left(1+\dfrac{2}{9}\right)=297\)

\(3^x.\dfrac{11}{9}=297\)

\(3^x=297:\dfrac{11}{9}=243=3^5\)

⇒\(x=5\)

Đáp án B

PT ⇔ 2 x − 6 x + 2.3 x − 2 = 0 ⇔ 2 x 1 − 3 x − 2 1 − 3 x = 0

⇔ 2 x − 2 1 − 3 x = 0 ⇔ x = 1 ∨ x = 0 .

Vậy tổng lập phương các nghiệm của PT trên bằng 1.

`4^(x+2) .3^x = 16.12^5`

`4^(x+2) .3^x = 4^2 . (3.4)^5`

`4^(x+2) .3^x = 4^2 . 3^5. 4^5`

`4^(x+2) .3^x = 4^7 . 3^5`

`4^(x+2) .3^x = 4^(5+2) . 3^5`

`x=5`

Ta có:4^x+2.3^x=16.12⁵

     ⇔ 4^x+2.3^x=4¹⁷.3¹⁵

      ⇔ 4^x+2:4¹⁷.3^x:3¹⁵=1

     ⇔ 4^x-15.3^x-15=1

     ⇔ 12^x-15=12⁰

     ⇔ x-15=0

     ⇔ x=15