x=2024 nên x-1=2023

\(H=x^{14}-2023x^{13}-2023x^{12}-...-2023x-2023\)

\(=x^{14}-x^{13}\left(x-1\right)-x^{12}\left(x-1\right)-...-x\left(x-1\right)-\left(x-1\right)\)

\(=x^{14}-x^{14}+x^{13}-x^{13}+x^{12}-...-x^2+x-x+1\)

=1

`12,45 . 157 – 12,45 . 57 + 3,7 . 17 – 3,7`

`=12,45.(157-57)+3,7.(17-1)`

`=12,45.100+3,7.16`

`=1245+59,2=1304,2`

`(x+1)(x+3)(x+5)(x+7)+15`

`=(x+1)(x+7)(x+3)(x+5)+15`

`= (x^2+7x+x+7)(x^2+5x+3x+15)+15 `

`=(x^2 +8x+7)(x^2+8x+15)+15`

Đặt `t=x^2 +8x+11`

`=(t-4)(t+4)+15`

`=t^2 -16 +15`

`=t^2 -1`

`=(t-1)(t+1)`

`=(x^2 +8x+11-1)(x^2 +8x+11+1)`

`=(x^2 +8x+10)(x^2 +8x+12)`

2x³ - 5x² + 8x - 3

= 2x³ - x² - 4x² + 2x + 6x - 3

= (2x³ - x²) - (4x² - 2x) + (6x - 3)

= x²(2x - 1) - 2x(2x - 1) + 3(2x - 1)

= (2x - 1)(x² - 2x + 3) 

a: ĐKXĐ: \(x\notin\left\{0;2\right\}\)

b: \(C=\dfrac{x^2}{x-2}\cdot\left(\dfrac{x^2+4}{x}-4\right)+3\)

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

\(=\dfrac{x^2\left(x-2\right)^2}{x\left(x-2\right)}+3=x\left(x-2\right)+3=x^2-2x+3\)

=2x1x3x21​+2x2x3x31​+2x3x3x41​+...+2x18x3x191​+2x19x3x201​=

=12𝑥3𝑥(11𝑥2+12𝑥3+13𝑥4+...+118𝑥19+119𝑥20)==2x31​x(1x21​+2x31​+3x41​+...+18x191​+19x201​)=

=16𝑥(2−11𝑥2+3−22𝑥3+4−33𝑥4+...+20−1919𝑥20)==61​x(1x22−1​+2x33−2​+3x44−3​+...+19x2020−19​)=

=16𝑥(1−12+12−13+13−14+...+119−120)==61​x(1−21​+21​−31​+31​−41​+...+191​−201​)=

=16𝑥(1−120)=16𝑥1920=19120=61​x(1−201​)=61​x2019​=12019​

a; b; c  bất kì thế c,  b đâu em nhỉ?

a: \(S_{ABC}=3\times S_{BCE}\)

=>\(S_{BCE}=\dfrac{45}{3}=15\left(cm^2\right)\)

=>\(S_{ABE}=45-15=30\left(cm^2\right)\)