Question

cho f(x) = ax^2 + bx +c biết 2a+b = 0  . chưng s minh f(-1) * f(3) >=0

Answer 1

f(-1)=a-b+c

f(3)=9a+3b+c

f(3)-f(-1)=8a+b=4(2a+b)

Mà 2a+b=0 =) f(3)-f(-1)=0

=) f(3)=f(-1) =) f(3).f(-1)=(a-b+c)^2

Mà (a-b+c)^2 >= 0 =) f(-1).f(3)>=0

Answer 2

Ta có : f(x) = ax² + bx + c

=> f( -1 ) = a - b + c

    f(3) = 9a + 3b + c

=> f(3) - f( -1 ) = 8a + 4b = 4 ( 2a + b ) = 4.0 = 0

=> f(3) = f( -1 )

=> f( -1 ). f(3) = f(3). f(3) = [ f(3) ]² \(\ge\) 0

=> đpcm

Study well ! >_<