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
Consider an acute triangle ABC of area S. Let CD vuong goc AB(D thuoc AB), DM vuong goc AC (M thuoc AC) and DN vuong goc BC(N thuoc BC). Denote by H1 and H2 the orthocentres of the triangle MNC, MND respectively. Find the area of the qudrilateral AH1BH2 in terms of S.
Let and distinct satisfy the conditions .
Find .
Answer:
Find the maximum value of $$ , x,y,z > 0
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?
From 0,1,2,3,4 and 5, we choose two different number x and y . what is the largest possible value of \(2\left(x+y\right)^2+\left(x-y\right)^2\)
In triangle ABC the points D and E are the intersections of the angular bisectors from C and B with the sides AB and AC respectively. Points F and G on the extentions of AB and AC beyond B and C respectively, satisfy BF= CG= BC. Prove that FG//DE.
Write the complete sentences:
1) The ambulance / be here / a few minutes
2) I / pleased that / you want / know more
3) Ba / taking a shower / 8.00 / last night
4) It / difficult / learn English
5) Would you / lending me / dictionary?
6) They / playing tennis / 10.30 / yesterday morning
7) Bao / always forgetting / homework
8) Last week / she / an English test / Friday
9) The school festival / held / the yard / last week
10) In / rice cooking festival / fire / made / traditional way
11) It / not difficult / translate / this sentence / English
12) You / mind / lend / me / dictionary?
13) New bicycles / make / Japan / be / expensive8
14) The Robinson family / making / preparation / Tet
15) You / mind / if / wait / me / moment?
16) Who / man / waiting outside?
17) There / some children / swim / the river
8) You / visited / Bach Ma Mountain?
19) We / can see / boy / ride / water buffalo
20) My Son / recognize / world heritage / 1999
21) They / be / vacation / Da Lat now
22) I / Mai whether / it was / highest building.
23) People / shoes / made / old car tires.
24) Thanks / the flowers / you / me / last week.
25) I asked / Thanh / whether / Petronas Twin Tower / the tallest building / the word
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