rut gon bieu thuc sau : (-12).(-2)-[|-3|^2-(-2)^3.3]/(-3)^3
Bai 1: Rut gon bieu thuc sau
B=(2/3)^3×(-3/4)^4×(-1)^5/(2/5)^2 × (-5/12)^3
Bai 2: Tim ia tri bieu thuc sau
M= 512- 512/2- 512/2^2- 512/2^2 - 512/2^3...512/2^10
Rut gon bieu thuc:
(3√2+√10)×√(38-12√5)
Rut gon bieu thuc sau
3(2*2+1)(2*4+1)(2*8+1)(2*16+1)
Rut gon bieu thuc B=3/2-(3/2)^2+(3/2)^3-.........(3/2)^2014
Ta có :\(B=\frac{3}{2}-\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3-....-\left(\frac{3}{2}\right)^{2014}\)
\(\frac{3}{2}B=\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^3+\left(\frac{3}{2}\right)^4-...+\left(\frac{3}{2}\right)^{2014}-\left(\frac{3}{2}\right)^{2015}\)
\(\frac{3}{2}B+B=\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^3+..+\left(\frac{3}{2}\right)^{2014}-\left(\frac{3}{2}\right)^{2015}\) \(+\frac{3}{2}-\left(\frac{3}{2}\right)^2+\left(\frac{3}{2}\right)^3-...-\left(\frac{3}{2}\right)^{2014}\)
\(\frac{5}{2}B=\frac{3}{2}-\left(\frac{3}{2}\right)^{2015}\)
\(B=\frac{\frac{3}{2}-\left(\frac{3}{2}\right)^{2015}}{\frac{5}{2}}\)
rut gon bieu thuc (2x+3) mũ 2 +(2x+5) mũ 2
Lời giải:
$(2x+3)^2+(2x+5)^2=4x^2+12x+9+4x^2+20x+25$
$=8x^2+32x+34$
Cho bieu thuc:
P=\(\frac{1}{\sqrt{x}+2}-\frac{5}{x-\sqrt{x}-6}-\frac{\sqrt{x}-2}{3-\sqrt{x}}\)
a. Rut gon bieu thuc P
b.Tim GTLN cua P sau khi rut gon
đk: x>=0; x khác 3
a) \(P=\frac{\sqrt{x}-3}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}-\frac{5}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}+\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{\sqrt{x}-3}=\frac{\sqrt{x}-3-5+x-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\frac{x+\sqrt{x}-12}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\)
\(P=\frac{\left(\sqrt{x}+4\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}=\frac{\sqrt{x}+4}{\sqrt{x}+2}\)
b) \(P=\frac{\sqrt{x}+2+2}{\sqrt{x}+2}=1+\frac{2}{\sqrt{x}+2}\)
ta có: \(x\ge0\Rightarrow\sqrt{x}\ge0\Leftrightarrow\sqrt{x}+2\ge2\Leftrightarrow\frac{2}{\sqrt{x}+2}\le1\Leftrightarrow1+\frac{2}{\sqrt{x}+2}\le2\Rightarrow MaxP=2\Rightarrow x=0\)
rut gon bieu thuc [(x^3+y^3)-2(x^2-y^2)+3(x+y)^2]:(x+y)
rut gon bieu thuc :P=5x(x-3)(x+3)-(2x-3)^2+34x(x+2)-5(x+2)^3+25x-1
\(:P=5x(x-3)(x+3)-(2x-3)^2+34x(x+2)-5(x+2)^3+25x-1\)
\(P=5x(x^2-9)-(4x^2-12x+9)+34x^2+68x-5(x^3+6x^2+12x+8)+25-1\)
\(P=5x^3-45x-4x^2+12x-9+34x^2+68x-5x^3-30x^2-60x-40+25-1\)
\(P=(5x^3-5x^3)+(34x^2-4x^2-30x^2)+(12x-45x++68x+25x-60x)-(9+1)\)
\(P=-10\)
Rut gon bieu thuc sau: 2x*(2x-1)2-3x*(x+3)2-4x*(x+1)2