Question

rezolvări ecuatia 9 la puterea x +2*3 la puterea x=99

Answer 1

Salut!
^=ridicare la putere
9^x+2*3^x=99
3^2x+2*3^x=99
3^x(3^x+2)=3^2*11
⇒3^x=3^2 ⇒ x=2
verificare:9^2+2*3^2=99
81+2*9=81+18=99

Answer 2

9^x+2*3^x=99
(3^2)^x+2*3^x=99
3^2x+2*3^x=99
3^2*3^x+2*3^x=99
9*3^x+2*3^x=99
Notam 3^x=a
=>9a+2a=99
11a=99
a=99:11=9
a=3^x
=> 3^x=9=3^2
=> x=2

VERIFICARE:
9^2+2*3^2=99
81+2×9=99
81+18=99
99=99