Toán

=>x^2+5x-2=x^2-2x+1 và x>=1

=>5x-2=-2x+1 và x>=1

=>7x=3 và x>=1

=>x=3/7(loại)

6:

\(\dfrac{2}{x-3}+\dfrac{2x}{x^2-4x+3}+\dfrac{x}{x-1}\)

\(=\dfrac{2\left(x-1\right)+2x+x\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}\)

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

\(=\dfrac{\left(x+2\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}=\dfrac{x+2}{x-3}\)

7: \(=\dfrac{\left(x+3\right)\left(x-3\right)+x^2-9}{x\left(x-3\right)}=\dfrac{x^2-9+x^2-9}{x\left(x-3\right)}\)

\(=\dfrac{2\left(x-3\right)\left(x+3\right)}{x\left(x-3\right)}=\dfrac{2x+6}{x}\)

8: \(=\dfrac{2\left(6x-5\right)}{\left(x-5\right)^2}+\dfrac{3x}{x-5}+\dfrac{x-2}{x+5}\)

\(=\dfrac{2\left(6x-5\right)\left(x-5\right)+3x\left(x^2-25\right)+\left(x-2\right)\left(x^2-10x+25\right)}{\left(x-5\right)^2\left(x+5\right)}\)

\(=\dfrac{2\left(6x^2-35x+25\right)+3x^3-7x+x^3-10x^2+25x-2x^2+20x-50}{\left(x-5\right)^2\cdot\left(x+5\right)}\)

\(=\dfrac{4x^3-12x^2+38x-50+12x^2-70x+50}{\left(x-5\right)^2\left(x+5\right)}\)

\(=\dfrac{4x^3-32x}{\left(x-5\right)^2\left(x+5\right)}\)

10: \(=\dfrac{6x+5x\left(x+3\right)+x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\)

\(=\dfrac{6x+5x^2+15x+x^2-3x}{\left(x-3\right)\left(x+3\right)}=\dfrac{6x^2+18x}{\left(x-3\right)\left(x+3\right)}=\dfrac{6x}{x-3}\)

a: Chiều rộng là 20*4/5=16m

Chu vi là (20+16)*2=64m

Diện tích là 16*20=320m²

b: Diện tích hồ cá là 18*10/2=90m²

Diện tích phần còn lại là:

320-90=230m²

c: Số viên gạch cần dùng là:

230*10^4:30^2\(\simeq2555,6\left(viên\right)\)

=>Cần dùng ít nhất là 2556 viên

=(5425+2430-3855):5=4000:5=800

a: Khi m=-1 thì phương trình sẽ là:

x^2-(-3-1)x+2-1-1=0

=>x^2+4x=0

=>x=0 hoặc x=-4

Cần gấp

a: 95;191; 383

f: 132; 182; 240

a: 95;191; 383

f: 132; 182; 240

a: \(=\dfrac{2}{5}\cdot2\sqrt{5}-\left|2-\sqrt{5}\right|\)

\(=\dfrac{4}{5}\sqrt{5}-\sqrt{5}+2=-\dfrac{1}{5}\sqrt{5}+2\)

b: \(=\dfrac{4\left(3+\sqrt{7}\right)}{9-7}-\dfrac{3\left(\sqrt{7}+2\right)}{7-4}\)

\(=2\left(3+\sqrt{7}\right)-\sqrt{7}-2\)

\(=6+2\sqrt{7}-\sqrt{7}-2=\sqrt{7}+4\)

c: \(=3\cdot2\sqrt{13}-2\cdot\left(\sqrt{13}-3\right)-\dfrac{3\left(4-\sqrt{13}\right)}{16-13}\)

\(=6\sqrt{13}-2\sqrt{13}+6-4+\sqrt{13}\)

\(=5\sqrt{13}+2\)

a) \(A=\dfrac{2}{5}\cdot\sqrt{20}-\sqrt{\left(2-\sqrt{5}\right)^2}\)

\(A=\dfrac{2}{5}\cdot2\sqrt{5}-\left|2-\sqrt{5}\right|\)

\(A=\dfrac{4}{5}\sqrt{5}+2-\sqrt{5}\)

\(A=-\dfrac{1}{5}\sqrt{5}+2\)

b) \(B=\dfrac{4}{3-\sqrt{7}}-\dfrac{3}{\sqrt{7}-2}\)

\(B=\dfrac{4\left(3+\sqrt{7}\right)}{\left(3-\sqrt{7}\right)\left(3+\sqrt{7}\right)}-\dfrac{3\left(\sqrt{7}+2\right)}{\left(\sqrt{7}-2\right)\left(\sqrt{7}+2\right)}\)

\(B=\dfrac{4\left(3+\sqrt{7}\right)}{9-7}-\dfrac{3\left(\sqrt{7}+2\right)}{7-4}\)

\(B=2\left(3+\sqrt{7}\right)-\left(\sqrt{7}+2\right)\)

\(B=6+2\sqrt{7}-\sqrt{7}-2\)

\(B=\sqrt{7}+4\)

c) \(C=3\sqrt{52}-2\sqrt{\left(3-\sqrt{13}\right)^2}-\dfrac{3}{4+\sqrt{13}}\)

\(C=3\cdot2\sqrt{13}-2\left|3-\sqrt{13}\right|-\dfrac{3\left(4-\sqrt{13}\right)}{\left(4-\sqrt{13}\right)\left(4+\sqrt{13}\right)}\)

\(C=6\sqrt{13}+2\left(3-\sqrt{13}\right)-\dfrac{3\left(4-\sqrt{13}\right)}{16-13}\)

\(C=6\sqrt{13}+6-2\sqrt{13}-4+\sqrt{13}\)

\(C=5\sqrt{13}+2\)