Ta có :
\(A=h\left(h+1\right)\left(h+2\right)\left(h+3\right)\)
\(=h\left(h+3\right)\left(h+1\right)\left(h+2\right)\)
\(=\left(h^2+3h\right)\left(h^2+3h+2\right)\)
\(=\left(h^2+3h+1-1\right)\left(h^2+3h+1+1\right)\)
\(=\left(h^2+3h+1\right)^2-1\)
Do : \(\left(h^2+3h+1\right)^2\ge0\Rightarrow\left(h^2+3h+1\right)^2-1\ge-1\)
Vậy \(MIN_A=-1\)
A = h( h + 1)( h + 2)( h + 3)
A = ( h2 + 3h)( h2 + 3h + 2)
Đặt : h2 + 3h + 1 = a , ta có :
A = ( a - 1)( a + 1)
A = a2 - 1
Thay : h2 + 3h + 1 = a , ta có :
A = ( h2 + 3h + 1 )2 - 1
=> Amin = -1 khi : ( h + \(\dfrac{3}{2}\))2 - \(\dfrac{5}{4}\) = 0 <=> h + \(\dfrac{3}{2}\) = \(\dfrac{\sqrt{5}}{2}\) <=>h= \(\dfrac{\sqrt{5}-3}{2}\)
