2 replies to this topic

[angel123]

Chứng minh các đẳng thức sau:

a, Nếu $a = b + 1$ thì $(a + b)(a^2 + b^2)(a^4 + b^4)(a^8 + b^8)...(a^{32} + b^{32}) = a^{64} - b^{64}$

b, Nếu $a = b + c$ thì $ \frac{(a^3 + b^3)}{(a^3 + c^3)} = \frac{(a + b)}{(a + c)}$

Edited by tienduc, 03-07-2017 - 15:36.

[trieutuyennham]

a)

Ta có 

(a+b)(a²+b²)...(a³²+b³²)=(a-b)(a+b)(a²+b²)...(a³²+b³²)=(a²-b²)(a²+b²)...(a³²+b³²)=a⁶⁴-b⁶⁴

[trieutuyennham]

b)

Ta có 

$\frac{a^{3}+b^{3}}{a^{3}+c^{3}}=\frac{a+b}{a+c}$

$\Leftrightarrow a^{2}-ab+b^{2}=a^{2}-ac+c^{2}$

$\Leftrightarrow (b-c)(b+c-a)=0$(đúng) suy ra đpcm