Question

cho\(\frac{a}{b}=\frac{c}{d}\) CMR\(\left(\frac{a}{c}\right)^n=\frac{a^n+b^n}{c^n+d^n}\)

Answer 1

a/b = c/d => a/c=b/d

Đặt a/c=b/d = k

=> a=ck ; b=dk

Khi đó : (a/c)ⁿ = kⁿ

aⁿ+bⁿ/cⁿ+dⁿ = cⁿkⁿ+dⁿkⁿ/cⁿ+dⁿ = kⁿ.(cⁿ+dⁿ)/cⁿ+dⁿ = k^n

=> (a/c)ⁿ = aⁿ+bⁿ/cⁿ+dⁿ

=> ĐPCM

k mk nha