Given the equation \(\frac{3}{x-3}\)- \(\frac{5}{x-5}\) = \(\frac{4}{x-4}\)- \(\frac{6}{x-6}\). The average (arithmetic mean ) of all roots of this equation is.....
1. Find x, given that:
\(\left(x+\frac{1}{3}\right)+\left(x+\frac{3}{40}\right)+\left(x+\frac{3}{88}\right)=\frac{31}{22}\)
2. The arithmatic average of three numbers is equal to 13.5 . The average of the first number and second number is 13, and the average of the second number and third number is 13.85 . Find the three numbers.
3. Compare A and B, given that:
A = 2.015 x 201.7
B = 20.16 x 20.16
It is known that the roots of the equation \(3x^5+9x^4-6x^2+5x-7=0\)are all integers.How many distinct roots does the equation have
Let a,b be the roots of equation \(x^2-px+q=0\) and let c,d be the roots of the equation \(x^2-rx+s=0\), where p,q,r,s are some positive real numbers. Suppose that :
\(M=\frac{2\left(abc+bcd+cda+dab\right)}{p^2+q^2+r^2+s^2}\)
is an integer. Determine a,b,c,d .
Let a,b be the roots of equation \(x^2-px+q=0\) and let c,d be the roots of the equation \(x^2-rx+s=0\), where p,q,r,s are some positive real numbers. Suppose that :
\(M=\frac{2\left(abc+bcd+cda+dab\right)}{p^2+q^2+r^2+s^2}\)
is an integer. Determine a,b,c,d .
Ta có:
\(\hept{\begin{cases}ab=q\\a+b=p\end{cases}}\)và \(\hept{\begin{cases}cd=s\\c+d=r\end{cases}}\)
\(M=\frac{2\left(abc+bcd+cda+dab\right)}{p^2+q^2+r^2+s^2}=\frac{2\left(qc+sb+sa+qd\right)}{p^2+q^2+r^2+s^2}\)
\(=\frac{2\left(qr+sp\right)}{p^2+q^2+r^2+s^2}\le\frac{2\left(qr+sp\right)}{2\left(qr+sp\right)}=1\)
Với M = 1 thì \(\hept{\begin{cases}q=r\\p=s\end{cases}}\)
Tới đây thì không biết đi sao nữa :D
thôi bỏ bài này đi cũng được vì chưa tới lúc cần dung phương trình
Given the equation (x - m)(m - 1) + (x - 1)(m + 1) = -2m. Find all values of m such that this equation has no solution. Answer: m = ...........
Given that
\(\frac{1}{x-1}-\frac{1}{x+1}-\frac{2}{x^2+1}-\frac{4}{x^4+1}-\frac{8}{x^8+1}-\frac{16}{x^{16}+1}=\frac{a}{x^{32}-1}\)
for all \(x\ne-1;1\).What is the value of a ?
the sum of roots of the equation /x-1/=/5-2x/
"/" là giá trị tuyệt đối
Có 2 trường hợp
x-1=5-2x \(\Rightarrow\)x=2
-x+1=-5+2x\(\Rightarrow\)x=-2
Tổng các nghiệm trên = 0
Khoa Trần trả lời sai rồi đáp án là 6 mới đúng
the product of roots of equation x(x-2016)(x+2017)=0
The product of roots of the equation :
X(X-2016)(X+2017)=0
\(x\left(x-2016\right)\left(x+2017\right)=0\)
\(\Rightarrow\)x=0 hoặc x-2016=0 hoặc x+2017=0
\(\Rightarrow\)x=0 hoặc x=2016 hoặc x=-2017