Math Problems
#Problems #Quest76
#Solutions | #Quest76
deg(P(x))=1 => P(x)=kx+c
For all x€R P(x) increasing.
Therefore max(P(x))=kb+c
min(P(x))=ka+c
maxP(x)-minP(x)=k(b-a) (1)
we have
maxP(x)-minP(x)=b-a (2)
From (1) and (2)
k(b-a)=b-a => k=1
P(x)=kx+c=x+c
c€R.
Answer: x+c , c€R
Author:Jamshidbek Hasanov
deg(P(x))=1 => P(x)=kx+c
For all x€R P(x) increasing.
Therefore max(P(x))=kb+c
min(P(x))=ka+c
maxP(x)-minP(x)=k(b-a) (1)
we have
maxP(x)-minP(x)=b-a (2)
From (1) and (2)
k(b-a)=b-a => k=1
P(x)=kx+c=x+c
c€R.
Answer: x+c , c€R
Author:
Math Problems
#Problems #Quest83
#Solutions | #Quest83
Any root of the equation of x³-x+1=0 satisfies the below equation :
p⁸=p⁹/p=(p-1)³/p=p²-3p+3-1/p
Thus
S=a⁸+b⁸+c⁸
S=(a²+b²+c²)-3(a+b+c)-(1/a+1/b+1/c)+9
From the equation and vieta,we can know that
a+b+c=0 , ab+bc+ac=-1 , abc=-1
Therefore
S=2-1+9=10
Author:@A_T_Uzbekistan
Any root of the equation of x³-x+1=0 satisfies the below equation :
p⁸=p⁹/p=(p-1)³/p=p²-3p+3-1/p
Thus
S=a⁸+b⁸+c⁸
S=(a²+b²+c²)-3(a+b+c)-(1/a+1/b+1/c)+9
From the equation and vieta,we can know that
a+b+c=0 , ab+bc+ac=-1 , abc=-1
Therefore
S=2-1+9=10
Author: