Question

cho a^2 - b^2 = 4c^2 CM hằng đẳng thức

(5a-3b+8c)(5a-3b-8c)=(3a-5b)^2

Giải CHI TIẾT giúp nha

Answer 1

Giải:

Ta có:

\(VT=\left(5a-3b+8c\right)\left(5a-3b-8c\right)\)

\(=\left(5a-3b\right)^2-\left(8c\right)^2\)

Mà \(a^2-b^2=4c^2\) nên:

\(VT=25^2-30ab+9b^2-16\left(a^2-b^2\right)\)

\(=9a^2-30ab+25b^2\)

\(=\left(3a-5b\right)^2=VP\) (Đpcm)

Answer 2

Ta có:
A = (5a – 3b + 8c)(5a – 3b –8c)
= (5a –3b)² – (8c)²
= (25a² – 30ab +9b²) – 64c²
Mà theo đề thì 4c² = a² –b²
Nên ta suy ra:
A = (25a² – 30ab +9b²) – 16(a² –b²)
= 9a² –30ab +25b²
= (3a –5b)²

Answer 3

Ta có:

\(\left(\left(5a-3b\right)+8c\right).\left(\left(5a-3b\right)-8c\right)=\left(3a-5b\right)^2\)

\(\Leftrightarrow\) \(\left(5a-3b\right)^2-\left(8c\right)^2=\left(3a-5b\right)^2\)

Ta có: \(a^2-b^2=4c^2\) \(\Leftrightarrow\) \(16\left(a^2-b^2\right)=64c^2=\left(8c\right)^2\)

\(\Rightarrow\) VT= \(\left(5a-3b\right)^2-16\left(a^2-b^2\right)\)

= \(25a^2-30ab+9b^2-16a^2+16b^2\)

= \(9a^2-30ab+25b^2\)

= \(\left(3a-5b\right)^2\)

\(\Rightarrow\) đpcm