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<c<d be integers. If one of the roots pf the equation (x-a)(x-b)(x-c)(x-d) - 9 is x=7, what is a+b+c+d?
Find n if n and \(n^3+2n^2+2n+4\) are both perfect square numbers
find the value of n such that the polynomial 2x^5 - 3x^3 + x^2 +n is divisible by the polynomial x+2
What is the largest integer n that satisfies (100^2-99^2)(99^2-98^2)...(3^2-2^2)(2^2-1^2) is divisible by 3^n?
1. Determine all pairs of integer (x;y) such that 2xy2+x+y+1=x2+2y2+xy
2. Let a,b,c satisfies the conditions
{
5≥a≥b≥c≥0
a+b≤8
a+b+c=10
Prove that 2a2+b2+c2≤38
3. Let a nad b satis fy the conditions
{
a3−6a2+15a=9
b3−3b2+6b=−1
Find the value of(a−b)2014 ?
4. Find the smallest positive integer n such that the number 2n+28+211 is a perfect square
I) THỰC HIỆN PHÉP TÍNH
a) 2x(x^2-4y)
b)3x^2(x+3y)
c) -1/2x^2(x-3)
d) (x+6)(2x-7)+x
e) (x-5)(2x+3)+x
II phân tích đa thức thành nhân tử
a) 6x^2+3xy
b) 8x^2-10xy
c) 3x(x-1)-y(1-x)
d) x^2-2xy+y^2-64
e) 2x^2+3x-5
f) 16x-5x^2-3
g) x^2-5x-6
IIITÌM X BIẾT
a)2x+1=0
b) -3x-5=0
c) -6x+7=0
d)(x+6)(2x+1)=0
e)2x^2+7x+3=0
f) (2x-3)(2x+1)=0
g) 2x(x-5)-x(3+2x)=26
h) 5x(x-1)=x-1
IV TÌM GTNN,GTLN.
a) tìm giá trị nhỏ nhất
x^2-6x+10
2x^2-6x
b) tìm giá trị lớn nhất
4x-x^2-5
4x-x^2+3
tìm x:
a) x(2x - 3) - 2(3-2x) = 0
b) 2x(x - 5) - x(3+2x) = 26
1. tìm x
a) x2(2x-3)-12+8x=0
b) 2(x+5)(2x-5)+(x-1)(5-2x)=0
c) 2x3-32x=0