let p(x) be a real polynomial of degree 2015. suppose that P(n) =n/n+1 for all n=0;1;2;...;2015
The value of P(2016) is .........
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Let P(x) be a polynomial of degree 2015. Suppose P(n)=\(\dfrac{n}{n+1}\) for all n =0, 1, 2, ..., 2015. Find the value of P(2016)
let P(x) be a polynomial of degree 3 and x1, x2, x3 are the solutions of P(x)=0. let \(\frac{P\left(\frac{1}{3}\right)-P\left(\frac{-1}{3}\right)}{P\left(0\right)}=8,\frac{P\left(\frac{1}{4}\right)-P\left(\frac{-1}{4}\right)}{P\left(0\right)}=9\)and x1+x2+x3 = 35. find the value of \(\frac{x2+x3}{x1}+\frac{x1+x3}{x2}+\frac{x1+x2}{x3}\)
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 .
find the value of n such that the polynomial 2x^5 - 3x^3 + x^2 +n is divisible by the polynomial x+2
tìm giá trị của n sao cho đa thức 2x ^ 5 - 3x ^ 3 + x ^ 2 + n chia hết cho đa thức x + 2
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Let N be the langest number ò region that can be formed by drawing 2016 straight lines on a plane. Find the sum ò all digits of N.
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
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thôi bỏ bài này đi cũng được vì chưa tới lúc cần dung phương trình
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câu 1: A rectangle has a length of 60cm and a width of 30cm. It is cut into 2 indentical squares, 2 identical rectangles and a shaded small square. Find the area of the shaded square.
Find the area of the shaded square.
câu 2.The number of ordered pairs (x; y) where x, y ∈ N* such that x2y2 - 2(x + y) is perfect square is ..........
câu 3.Let ABCD be the square with the side length 56cm. If E and F lie on CD, C respectively such that CF 14cm and EAF 45o then CE ........cm.
câu 4.
Given P...
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câu 1: A rectangle has a length of 60cm and a width of 30cm. It is cut into 2 indentical squares, 2 identical rectangles and a shaded small square. Find the area of the shaded square.
Find the area of the shaded square.
câu 2.The number of ordered pairs (x; y) where x, y ∈ N* such that x2y2 - 2(x + y) is perfect square is ..........
câu 3.Let ABCD be the square with the side length 56cm. If E and F lie on CD, C respectively such that CF = 14cm and EAF = 45o then CE = ........cm.
câu 4.
Given P(x) = (x2 - 1/2 x - 1/2)1008
If P(x) = a2016x2016 + a2015x2015 + ..... + a1x + a0
then the value of the sum a0 + a2 + a4 + .... + a2014 is ...........
Find the value of P = k(x1) x k(x2) x k(x3) x k(x4) x k(x5) câu 8.The smallest value of
is .............
câu 9.Let ABCD be a trapezoid with bases AB, CD and O be the intersection of AC and BD. If the areas of triangle OAB, triangle OCD are 16cm2, 40cm2respectively and M is the midpoint of BD, then the area of the triangle AMD is .........cm2.
câu 10.Bottle A contains 15% syrup. Bottle B contains 40% syrup. When these 2 bottles of syrup are mixed, the syrup content is 30% and the total volume is 600ml. How much syrup is in the bottle A at first?
câu 11.Let ABCD.A'B'C'D' be a cube with AC' = √3cm. Find the total surface area of this cube.
câu 12.Let ABC be a triangle with AB = 3cm, AC = 7cm. The internal bisector of the angle BAC intersects BC at D. The line passing through D and parallel to AC cuts AB at E. Find the measure of DE.
câu 12.Given two numbers x, y such that (4y2 - 12y + 25)(4x2 + 6x + 4) = 28The ratio of y to x is ........ câu 13.Mr.Joseph drives car from A to B at a constant speed. If the speed of the car is increased by 20%, it takes him one hour less than the usual time. If he drives at the constant speed for the first 100km before increasing the speed by 30%, it also takes him one hour less than the usual. The distance of AB is ..........km. câu 14.A triangle ABC has  = 120o and the bisector AD (D ∈ BC). If AB = 40cm, AD = 30cm, then AC = ..... cm. câu 15.As shown in the figure, the length of BE is .............
câu 16.
Let f(x) the polynomial given by f(x) = (1 + 2x + 3x2 + 4x3 + 5x4 + 84x5)
Suppose that f(x) = ao + a1x + a2x2 + ..... + ..... + a50x50.
The value of T = a1 + a2 + .... + a50 is .........
The area of the trapezoid ABCD is .........cm2. câu 18.Find the least possible value of A = 4x2 - 3x + 1/4x + 2015, where x varies in the set of positive real numbers. The least possible value of A is câu 19.
Let f(x) the polynomial given by f(x) = (1 + 2x + 3x2 + 4x3 + 5x4 + 84x5)
Suppose that f(x) = ao + a1x + a2x2 + ..... + ..... + a50x50.
The value of T = a1 + a2 + .... + a50 is ......
Cách khai báo sau đây là đúng hay sai? Nếu sai hãy sửa lại:
Var x:array [10,13] of integer;
S:=0; n:=0; while S < for do n:=n + 1; S:= s+n
For i:=1 to 10 do; writeln ('A')
Var x: real; begin for x:=1 to 10 do writeln ('A'); end.
A/ Sai.
Sửa: Var x:array[10..13] of integer;
B/ Sai.
Sửa: S:= 0; n:= 0; while S < 50 do
begin n:= n + 1; S:= S + n; end;
C/ Sai.
Sửa: for i:= 1 to 10 do writeln('A');
D/ Sai.
Sửa x: integer; begin for x:= 1 to 10 do writeln('A'); end.
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