tìm có mà link https://h7.net/hoi-dap/toan-8/phan-h-da-thuc-x-1-x-3-x-5-x-7-15-thanh-nhan-tu-faq257547.html
tí mình gửi qua cho
học tốt
\(B=\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)
\(=\left(x+1\right)\left(x+7\right)\left(x+3\right)\left(x+5\right)+15\)
\(=\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)(1)
Đặt \(x^2+8x+11=t\)thay vào (1) ta được :
\(\left(t-4\right)\left(t+4\right)+15\)
\(=t^2-16+15\)
\(=t^2-1\)
\(=\left(t-1\right)\left(t+1\right)\)Thay \(t=x^2+8x+11\)vào bt ta được:
\(\left(x^2+8x+11-1\right)\left(x^2+8x+11+1\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
\(=\left(x^2+8x+10\right)\left(x^2+2x+6x+12\right)\)
\(=\left(x^2+8x+10\right)\left[x\left(x+2\right)+6\left(x+2\right)\right]\)
\(=\left(x^2+8x+10\right)\left(x+2\right)\left(x+6\right)\)
Bài làm
B = ( x + 1 )( x + 3 )( x + 5 )( x + 7 ) + 15
B = [ ( x + 1 ) ( x + 7 ) ] [ ( x + 3 ) ( x + 5 ) ] + 15
B = [ x2 + 7x + x + 7 ] [ x2 + 5x + 3x + 15 ] + 15
B = [ x2 + 8x + 7 ] [ x2 + 8x + 15 ] + 15
Đặt [ x2 + 8x + 7 ] [ x2 + 8x + 15 ] + 15 = k
=> B = k . ( k + 8 ) + 15
=> B = k2 + 8k + 15
=> B = k2 + 3k + 5k + 15
=> B = ( k2 + 5k ) + ( 3k + 15 )
=> B = [ k( k + 5 ) ] + [ 3( k + 5 ) ]
=> B = ( k + 5 ) ( k + 3 )
Hay B = ( x2 + 8x + 7 + 3 ) ( x2 + 8x + 7 + 5 )
=> B = ( x2 + 8x + 10 ) ( x2 + 8x + 12 )
=> B = ( x2 + 8x + 10 ) ( x2 + 2x + 6x + 12 )
=> B = ( x2 + 8x + 10 ) [ ( x2 + 6x ) + ( 2x + 12 )]
=> B = ( x2 + 8x + 10 ) [ x( x + 6 ) + 2( x + 6 ) ]
=> B = ( x2 + 8x + 10 ) ( x + 2 ) ( x + 6 )
# Học tốt #
\(\text{Ủa bài ày ó ong sách áo oaa è =)))}\)
\(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)
\(\left(x+1\right)\left(x+7\right)\left(x+3\right)\left(x+5\right)=15\)
\(\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\)
\(x^2+8x+11=t\)
\(\text{x là số cần tìm ta có }\)
\(x^2-16+15=x^2-1\)
\(\left(x-1\right)\left(x+1\right)\)
\(\left(x^2+8x+11-1\right)\left(x^2+8x+11+1\right)\)
\(\left(x^2+8x+10\right)\left(x^2+8x+12\right)\)
