10x-15-x^2=0
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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
`(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: \(C=\dfrac{x^2}{x-2}\cdot\left(\dfrac{x^2+4}{x}-4\right)+3\)
\(=\dfrac{x^2}{x-2}\cdot\dfrac{x^2-4x+4}{x}+3\)
\(=\dfrac{x^2\left(x-2\right)^2}{x\left(x-2\right)}+3=x\left(x-2\right)+3=x^2-2x+3\)
`10x-15-x^2=0`
`<=>-x^2 +10x -15=0`
`Δ=b^2 -4ac=10^2 -4.(-1).(-15)=40`
`x_1 =` \(\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-10+\sqrt{40}}{2.\left(-1\right)}=5-\sqrt{10}\)
`x_2 =` \(\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-10-\sqrt{40}}{2.\left(-1\right)}=5+\sqrt{10}\)