cho a2 - b2 = 4c2 Cm hang dang thuc:
(5a-3b+8c).(5a-3b-8c)= (3a-5b)2
Chung minh dang thuc
2bc+b^2+c^2-a^2=4m (m-a)
biet a+b+c=2m
(5a-3a+8c)×(5a-3b-8c)=(3a-5b)^2 biet a^2-b^2=4c^2
cho a^2 -b^2 =4c^2 cmr (5a-3b+8c) (5a-3b-8c)=(3a-5b)^2
Cho a2 - b2 = 4c2. Cm hằng đẳng thức:
(5a - 3b + 8c) (5a - 3b - 8c) = (3a - 5b)2
Lời giải:
\((5a-3b+8c)(5a-3b-8c)=(5a-3b)^2-(8c)^2\)
\(=25a^2+9b^2-30ab-(8c)^2\)
\(=(9a^2+25b^2-30ab)+(16a^2-16b^2)-64c^2\)
\(=(3a-5b)^2+16.4c^2-64c^2\)
\(=(3a-5b)^2\)
cho a^2-b^2=4c^2 .CMR:
(5a-3b+8c)(5a-3b-8c)=(3a-5b)^2
GIẢI NHANH GIÚP NHA CẦN GẤP
VT := [(5a - 3b) + 8c][(5a - 3b) - 8c]
= (5a - 3b)^2 - 64c^2 (theo hiệu hai bình phương)
= 25a^2 - 30ab + 9b^2 - 64c^2 (theo bình phương của hiệu)
= 25a^2 - 30ab + 9b^2 - 16(a^2 - b^2) (vì 4c^2 = a^2 - b^2)
= 9a^2 - 30ab + 25b^2
= (3a - 5b)^2 (theo bình phương của hiệu).
Cho a2 -b2 =4c2. Chứng minh rằng: (5a -3b +8c)( 5a -3b +8c) = (3a -5b)2
Cho a2-b2=4C2. CMR :
(5a-3b+8c) (5a-3b-8c)=(3a-5b)2
\(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(5a-3b\right)^2-\left(8c\right)^2\)
\(=25a^2-30ab+9b^2-16c^2\)
\(=25a^2-30ab+9b^2-16\left(a^2-b^2\right)\)
\(=25a^2-30ab+9b^2-16c^2+16b^2\)
\(=9a^2-30ab+25b^2\)
\(=\left(3a-5b\right)^2\)
Cho \(a^2-b^2=4c^2\).CMR : ( 5a - 3b + 8c ) (5a-3b-8c) = ( 3a - 5b )\(^2\)
\(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(3a-5b\right)^2\)
\(\Leftrightarrow\left(5a-3b\right)^2-64c^2-\left(3a-5b\right)^2=0\)
\(\Leftrightarrow\left(5a-3b-3a+5b\right)\left(5a-3b+3a-5b\right)=64c^2\)
\(\Leftrightarrow\left(2a+2b\right)\left(8a-8b\right)=16\left(a^2-b^2\right)\)
\(\Leftrightarrow16\left(a^2-b^2\right)=16\left(a^2-b^2\right)\left(true\right)\)
Vậy \(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(3a-5b\right)^2\)khi \(a^2-b^2=4c^2\)
Cho a2-b2=4c2. Chứng minh:
(5a-3b+8c)(5a-3b-8c)=(3a-5b)2
Ta có:
\(VT=(5a-3b+8c).(5a-3b-8c)\)
\(=\left(5a-3b\right)^2-\left(8c\right)^2\)
Mà \(a^2-b^2=4c^2\) nên:
\(VT=25^2-30ab+9b^2-16.\left(a^2-b^2\right)\)
\(=9a^2-30ab+25b^2\)
\(=\left(3a-5b\right)^2=VP\)
\(\Rightarrow\) Đpcm.
Cho a2 - b2= 4c2. Chứng minh rằng: (5a - 3b + 8c).(5a - 3b - 8c) = (3a - 5b)2
Ta có : \(\left(5a-3b+8c\right)\left(5a-3b-8c\right)\)
\(=\left(5a-3b\right)^2-\left(8c\right)^2\)
\(=\left(5a-3b\right)^2-64c^2\)
\(=\left(5a-3b\right)^2-16.4c^2\)
\(=\left(5a-3b\right)^2-16\left(a^2-b^2\right)\)
\(=25a^2-30ab+9b^2-16a^2+16b^2\)
\(=9a^2-30ab+25b^2\)
\(=\left(3a-5b\right)^2\left(đpcm\right)\)