19x2 + 28y2 = 729
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Ta có
1 9 x 2 - 1 64 y 2 = x 3 2 - y 8 2 = x 3 - y 8 x 3 + y 8
Đáp án cần chọn là: D
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7/19 . 1/3 + 7/19 . 2/3 =7/19 .(1/3 + 2/3)= 7/19 . 1 = 7/19
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\(a,x^4-4x^3-19x^2+106x-120=0\\ \Rightarrow\left(x-4\right)\left(x^3-19x+30\right)=0\Rightarrow\left(x-4\right)\left(x+5\right)\left(x^2-5x+6\right)=0\\ \Rightarrow\left(x-4\right)\left(x+5\right)\left(x-2\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=4\\x=-5\\x=2\\x=3\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{-5;2;3;4\right\}\)
\(b,4x^4+12x^3+5x^2-6x-15=0\\ \Rightarrow\left(x-1\right)\left(4x^3+16x^2+21x+15\right)=0\\ \Rightarrow\left(x-1\right)\left[\left(4x^3+10x^2\right)+\left(6x^2+15x\right)+\left(6x+15\right)\right]=0\\ \Rightarrow\left(x-1\right)\left[2x^2\left(2x+5\right)+3x\left(2x+5\right)+3\left(2x+5\right)\right]=0\\ \Rightarrow\left(x-1\right)\left(2x+5\right)\left(2x^2+3x+3\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{5}{2}\\2x^2+3x+3=0\left(vô.lí\right)\end{matrix}\right.\)
Vậy pt có tập nghiệm \(S=\left\{1;-\dfrac{5}{2}\right\}\)
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Đáp án C
Ta có F ' x = 1 27 3 e 3 x + 1 9 x 2 − 24 x + 17 + e 3 x + 1 18 x − 24 = 1 27 e 3 x + 1 27 x 2 − 54 x + 27
= e 3 x + 1 x 2 − 2 x + 1
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j: \(\dfrac{10x^3-19x^2-4x+4}{2x+1}\)
\(=\dfrac{10x^3+5x^2-24x^2-12x+8x+4}{2x+1}\)
\(=5x^2-12x+4\)
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\(\frac{3}{5}x\frac{8}{27}x\frac{5}{3}=\frac{3}{3}x\frac{5}{5}x\frac{8}{27}=\frac{8}{27}\)
\(\frac{7}{19}x\frac{1}{3}+\frac{7}{19}x\frac{2}{3}=\frac{7}{19}x\left(\frac{1}{3}+\frac{2}{3}\right)=\frac{7}{19}\)