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\(1,\frac{x+1}{x-2}=\frac{3}{4}\)
\(\Rightarrow3x-6=4x+4\)
\(\Rightarrow3x-4x=4+6\)
\(\Rightarrow-x=10\Leftrightarrow x=-10\)
\(2,\frac{x-1}{3}=\frac{x+3}{5}\)
\(\Rightarrow5x-5=3x+9\)
\(\Rightarrow5x-3x=9+5\)
\(\Rightarrow2x=14\Leftrightarrow x=7\)
\(3,\frac{2x+3}{24}=\frac{3x-1}{32}\)
\(\Rightarrow64x+96=72x-24\)
\(\Rightarrow72x-64x=24+96\)
\(\Rightarrow8x=120\)
\(\Rightarrow x=15\)
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a) Ta có: \(5x\left(\frac{1}{5}x-2\right)+3\left(6-\frac{1}{3}x^2\right)=12\)
\(\Leftrightarrow x^2-10x+18-x^2=12\)
\(\Leftrightarrow-10x+18=12\)
\(\Leftrightarrow-10x=-6\)
hay \(x=\frac{3}{5}\)
Vậy: \(x=\frac{3}{5}\)
b) Ta có: \(7x\left(x-2\right)-5\left(x-1\right)=7x^2+3\)
\(\Leftrightarrow7x^2-14x-5x+5-7x^2-3=0\)
\(\Leftrightarrow-19x+2=0\)
\(\Leftrightarrow-19x=-2\)
hay \(x=\frac{2}{19}\)
Vậy: \(x=\frac{2}{19}\)
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Giải :
\(\frac{x+1}{x-2}=\frac{3}{4}\)
\(\Rightarrow4.\left(x-1\right)=3.\left(x-2\right)\)
\(\Rightarrow4x-4=3x-6\)
\(\Rightarrow4x-4-3x+6=0\)
\(\Rightarrow x+2=0\)
\(\Rightarrow x=-2\)Không thỏa mãn => Không có giá trị x thỏa mãn đề bài
\(\frac{2x-3}{x+1}=\frac{4}{7}\)
\(\Rightarrow7.\left(2x-3\right)=4.\left(x+1\right)\)
\(\Rightarrow14x-21-4x-4=0\)
\(\Rightarrow10x-25=0\)
\(\Rightarrow10x=25\)
\(\Rightarrow x=\frac{25}{10}=\frac{5}{2}\)
Giá trị trên thỏa mãn đầu bài
Các phần khác em làm tương tự nha
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1) x2 - 5x +6= x2 -2x -3x +6 = x(x-2) -3(x-2)= (x-3)(x-2)
2) x2 +5x +6= x2 +2x+3x+6= x(x+2)+3(x+2)=(x+3)(x+2)
3) x2 -7x+12= x2 -3x-4x+12= x(x-3)-4(x-3)=(x-4)(x-3)
4) x2+7x+12= (x+3)(x+4) (bạn cũng làm tương tự như câu 3 chỉ đổi dấu thôi nhea)
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=>4x^3-7x^2-9x=0
=>x(4x^2-7x-9)=0
=>x=0 hoặc 4x^2-7x-9=0
=>\(x\in\left\{0;\dfrac{7+\sqrt{193}}{8};\dfrac{7-\sqrt{193}}{8}\right\}\)
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a) P - Q = \(\left(4x^3-7x^2+3x-12\right)-\left(-2x^3+7x^2-9x+12\right)\)
= \(4x^3-7x^2+3x-12+2x^3-7x^2+9x-12\)
= \(4x^3+2x^3-7x^2-7x^2+3x+9x-12-12\)
= \(6x^3+12x-24\)
c) P + Q = \(\left(4x^3-7x^2+3x-12\right)+\left(-2x^3+7x^2-9x+12\right)\)
= \(4x^3-7x^2+3x-12-2x^3+7x^2-9x+12\)
= \(4x^3-2x^3-7x^2+7x^2+3x-9x-12+12\)
= \(6x^3+14x^2-6x+24\)
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F(x)+G(x)=(-5x\(^5\)+7x^3+x^2-2x+12)+(-4x^4+x^3+7x^2+8x-9)
=(-5x^5)+(7x^3+x^3)+(x^2+7x^2)+(-2x+8x)+(
-4x^4)+(12+-9) =(-5x^5)+8x^3+8x^2+6x+(-4x^4)+3. CHÚC BẠN HỌC TỐT
F(x)+G(x)=(-5x3+7x3+x2-2x+12)+(-4x4+x3+7x2+8x-9)=-5x5-4x4+8x3+8x2+6x+3
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\(2\)
CMR
\(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+....+\frac{1}{49.50}=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\left(\frac{1}{1}+\frac{1}{3}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{49}+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{50}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{25}\)
\(=\frac{1}{26}+\frac{1}{27}+....+\frac{1}{50}\left(đpcm\right)\)