Question

Cho a,b,c,d khác 0 và b²=ac,c²=bd. Chứng minh : \(\frac{a^3 +b^3+c^3}{b^3+c^3+d^3}=\frac{a}{d}\)

Answer 1

ta có:

b^2=ac =>a/b=b/c  (1)

c^2=bd =>b/c=c/d  (2)

(1)(2)=>a/b=b/c=c/d

=>a^3/b^3=b^3/c^3=c^3/d^3=abc/bcd

=>(a^3+b^3+c^30)/(b^3+c^3+d^3)=a/d

Vay.......

Nhớ tick mk nha

Answer 2

ta có:

b^2=ac =>a/b=b/c  (1)

c^2=bd =>b/c=c/d  (2)

(1)(2)=>a/b=b/c=c/d

=>a^3/b^3=b^3/c^3=c^3/d^3=abc/bcd

=>(a^3+b^3+c^3)/(b^3+c^3+d^3)=a/d

Vay dpcm