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thanks, and another question

bluefiberglass(ricebox1/2)

There are two parts in this question.
a) Prove that if a quadratic equation has consective integers as its coefficients, then it has no real roots.
B), Prove or disprove the theorem that if a quadratic equation has three consecutive integers as its coefficients, then it has no real roots.

Well, I did the second part as :
the quadratic equation (n-1)x*x+nx+(n+1)=0, where n>=2.
then b*b-4ac<0,
it is true.

What should I write the first part? How to tell them apart?
Thanks again.

the third question is ' Prove that f(n)=n*n*n-n*n-4 is a composite number. (ie, not a prime number) for all integers n>2.

(#340474@0)
Last Updated: 2002-1-19
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工作学习 / 求学深造 / a math question thanks!! Suppose triangle ABC has side lengths a, b, c, Prove that if a*a+b*b+c*c=ab+bc+ac, then triangle ABC is an equilateral triangle. -bluefiberglass(ricebox1/2); 2002-1-19 (#340457@0)

in -blaise(); 2002-1-19 {149} (#340463@0)
a*a+b*b>=2*a*b;
b*b+c*c>=2*b*c;
c*c+a*a>=2*c*a;
each = is true only if x==y

2(a*a+b*b+c*c)>=2(a*b+b*c+c*d)

the = is true only if
a==b==c
thanks, and another question -bluefiberglass(ricebox1/2); 2002-1-19 {624} (#340474@0)
There are two parts in this question.
a) Prove that if a quadratic equation has consective integers as its coefficients, then it has no real roots.
B), Prove or disprove the theorem that if a quadratic equation has three consecutive integers as its coefficients, then it has no real roots.

Well, I did the second part as :
the quadratic equation (n-1)x*x+nx+(n+1)=0, where n>=2.
then b*b-4ac<0,
it is true.

What should I write the first part? How to tell them apart?
Thanks again.

the third question is ' Prove that f(n)=n*n*n-n*n-4 is a composite number. (ie, not a prime number) for all integers n>2.

n*n*n-n*n-4 =(n-2)*(n*n+n+2) -wxyz(wxyz); 2002-1-20 (#340746@0)
Why do you do such easy questions? n*n*n-n*n-4=(n-2)(n*n+n+2), so it is a composite number. -bigsquirrel(小松鼠); 2002-1-20 (#340763@0)

(a-b)**2+(b-c)**2+(c-a)**2=0 -wxyz(wxyz); 2002-1-19 {18} (#340478@0)
这可是基本功啊！！
2(a*a+b*b+c*c)=2*(ab+ba+ac) > (a-b)^2 + (b-c)^2+(a-c)^2=0 >a=b,b=c,a=c -winger1234(ben); 2002-1-19 (#340550@0)
too easy. a*a+b*b+c*c if and only if a=b=c>0, no matter a b c are the sides of a triangle or not. -bigsquirrel(小松鼠); 2002-1-20 (#340750@0)
你在上几年级？ -urfr(urfr); 2002-1-20 (#340764@0)

@Florida

thanks, and another question

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