Đáp án:
Giải thích các bước giải:
a) ( m + n ) 2 − ( m − n ) 2
= [ ( m + n ) − ( m − n ) ] [ ( m + n ) + ( m − n ) ]
= ( 2 n ) ( 2 m )
= 4 m n (m+n)2−(m−n)2
=[(m+n)−(m−n)][(m+n)+(m−n)]
=(2n)(2m)
=4mn ( m + n ) ( m − n )
= m 2 − n 2
B=( 2 x + 1 ) 2 + 2 ( 4 x 2 − 1 ) + ( 2 x − 1 ) 2 (2x+1)2+2(4x2−1)+(2x−1)2
= 4 x 2 + 4 x + 1 + 8 x 2 − 2 + 4 x 2 − 4 x + 1 4x2+4x+1+8x2−2+4x2−4x+1
= 16 x 2
Bài 10
A=x2−4x+1=(x2−4x+4)−3
=(x−2)2−3A=x2−4x+1
=(x2−4x+4)−3=(x−2)2−3
Vì (x−2)2≥0,∀x∈R(x−2)2≥0,∀x∈R nên A=(x−2)2−3≥0−3
=−3A=(x−2)2−3≥0−3=−3
Vậy Amin=−3Amin=−3
Giá trị này đạt tại (x−2)2=0⇔x=2
B=x15−8x14+8x13−8x2+...−8x2+8x−5B=x15−8x14+8x13−8x2+...−8x2+8x−5
=> B=x15−(x+1)x14+(x+1)x13−(x+1)x12+...+(x+1)x−x+2B=x15−(x+1)x14+(x+1)x13−(x+1)x12+...+(x+1)x−x+2
=>B=x15−x15+x14−x14+x13−x13−x12+...+x2+x−x+2B=x15−x15+x14−x14+x13−x13−x12+...+x2+x−x+2
=>B=2
