Question

tìm x biết

(2^x-8)³+(4^x+13)³=(4^x+2^x+5)³

giúp mình nhé mình xin cảm ơn

Answer 1

 (2^x-8)^3=(4^x+2^x+5)^3-(4^x+13)^3 
(2^x-8)^3=[(4^x+2^x+5)-(4^x+13)]*[(4^x... + (4^x+13)^2] 
(2^x-8)^3=(2^x-8)*[(4^x+2^x+5)^2+(4^x+... + (4^x+13)^2] 
2^x=8=>x=3 
hoặc (2^x-8)^2=(4^x+2^x+5)^2+(4^x+2^x+5)(4^x+... + (4^x+13)^2 
(4^x+2^x+5)^2 - (2^x-8)^2+(4^x+2^x+5)(4^x+13) + (4^x+13)^2=0 
[(4^x+2^x+5)-(2^x-8)]*[(4^x+2^x+5)+(2^... + (4^x+3)*[(4^x+2^x+5)+(4^x+13)]=0 
(4^x+13)*(4^x+2*2^x-3) + (4^x+3)*(2*4^x+2^x+18)=0 
(4^x+13)[(4^x+2*2^x-3) + (2*4^x+2^x+18)]=0 
4^x+13=0 (VN) 
hoặc 3*4^x + 3*2^x +15=0 
đặt t=2^x ( t>0) 
t^2 + t + 5=0 ptvn