=(x^2+x^2a+a+a^2+a^2x^2+1)/(x^2-x^2a-a+a^2+a^2x^2+1)
=\(\dfrac{x^2\left(1+a^2\right)+a^2+1+x^2a+a}{x^2+a^2x^2+a^2+1-x^2a-a}\)
\(=\dfrac{\left(1+a^2\right)\left(x^2+1\right)+a\left(x^2+1\right)}{x^2\left(1+a^2\right)+\left(a^2+1\right)-a\left(x^2+1\right)}\)
\(=\dfrac{\left(x^2+1\right)\left(a^2+a+1\right)}{\left(a^2+1\right)\left(x^2+1\right)-a\left(x^2+1\right)}=\dfrac{a^2+a+1}{a^2-a+1}\)
Tính GTCBT
\(A=\dfrac{4x^4+1}{4\left(x+1\right)^2}\cdot\dfrac{4\left(x+2\right)^2+1}{4\left(x+3\right)^4+1}\cdot\cdot\cdot\dfrac{4\left(x+10\right)^4+1}{4\left(x+11\right)^4+1}\)
Tại x =19,092014
Đặt ẩn phụ:
a, \(\left(x^2+3x+1\right)\cdot\left(x^2+3x-3\right)-5\)
b, \(\left(x^2+2x\right)^2-2x^2-4x-3\)
c, \(\left(x+1\right)\cdot\left(x+3\right)\cdot\left(x+5\right)\cdot\left(x+7\right)+15\)
d, \(x^2-2xy+y^2-7x+7y+12\)
Tính \(A=\left(1+\frac{2}{1\times4}\right)\left(1+\frac{2}{2\times5}\right)\left(1+\frac{2}{3\times6}\right)\cdot\cdot\cdot\left(1+\frac{2}{2019\times2022}\right)\)
Giúp tớ với
a)\(\frac{\left(x-4\right)^2}{7}-\frac{\left(x+4\right)^2}{5}\ge\frac{2\left(x^2-3\right)}{35}\)
b)\(\frac{\left(2x-1\right)^2}{2}-\frac{\left(2x+1\right)^2}{4}< \left(x-3\right)^2\)
c)\(|-5x+1|=6-3x\)
d)\(6\cdot|x+3|=-8x\)
e)\(7\cdot|x+1|=6-x\)
1)Giải pt: \(2\cdot\left(x+\dfrac{1}{x}\right)^2+\left(x^2+\dfrac{1}{x^2}\right)^2-\left(x^2+\dfrac{1}{x^2}\right)\cdot\left(x+\dfrac{1}{x}\right)^2=\left(x+2\right)^2\)
2)Giải pt: \(\dfrac{|3-2x|-|x|}{|2+3x|+x-2}=5\)
3)tìm tất cả các cặp số nguyên tố(x,y) là nghiệm của pt: x2 - 2y2 - 1=0
Nhìn bài toán xong còn bạn nào có thể làm cho mình ko
1. x=\(\sqrt{6+2\sqrt{2}\cdot\sqrt{3-\sqrt{\sqrt{2}+2\sqrt{3}+\sqrt{18-8\sqrt{2}}}}}-\sqrt{3}\)
2.Chứng minh: a + b + c = 2019 và \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=2019\) thì 1 trong 3 số phải có 1 số bằng 2019
3. Giải
a, \(\left|x-2\right|\cdot\left(x-1\right)\cdot\left(x+1\right)\cdot\left(x+2\right)=4\)
b, \(\frac{15x}{x^2-3x+4}=\frac{12}{x+4}+\frac{4}{x-1}+1\)
\(\dfrac{\left(\dfrac{2}{3}\right)^3\cdot\left(\dfrac{-3}{4}\right)^2\cdot\left(-1\right)^{2019}}{\left(\dfrac{2}{5}\right)^2\cdot\left(\dfrac{-5}{12}\right)^3}\)
Tính hộ mk với
Giaỉ các phương trình sau:
a) \(\left(x^2+11x+12\right)\left(x^2+9x+20\right)\left(x^2+13x+42\right)=36\left(x^2+11x+30\right)\left(x^2+11x+31\right)\)
b) \(20\left(\frac{x-2}{x+1}\right)^2-5\left(\frac{x+2}{x-1}\right)^2+48\cdot\frac{x^2-4}{x^2-1}=0\)
CMR:
a,\(x^2+y^2+z^2\ge\frac{1}{3}\left(x+y+z\right)^2\)
b,\(\left(x+y+z\right)^2\ge3\cdot\left(xy+yz+xz\right)\)
