Question

1,Rezolvati ecuatiile:

a) √2x-1 + √2x-x =2
b) ∛x-1 + ∛2x+1 =0

2.Rezolvati ecuatiile exponentiale:

a) 8^x=512
b) 2^x=243
c) √ 5^{x} = ∛625
d) 5 x^{2+1} =3125
e) (0,4)^x-4 = (6,25)^4x-7
f) (4/9)^x+3 · (27/8)^x =2/3
g) 3^x+1 + 3^x =108
h) 9^x - 10·3^x +9=0
i) 49^x - 35^x =25^x.

p.s. "^" = la puterea

Answer 1

1.a) sqrt(2x-1) + sqrt(2x-x) = 2  (sqrt inseamna radical)sqrt(2x-1) + sqrt(x) = 2 /^2  (/^2 inseamna ridicam la puterea a doua)2x-1 + 2sqrt[(2x-1)*x] + x = 43x + 2sqrt[2*x*x -x] = 52sqrt(2*x^2) = 5-3x /^24 * 2*x*x = 25 - 30x + 9x8x^2 + 21x - 25 = 0delta = 21*21 + 800 = 441 + 800 = 1241x1 = (-21 + sqrt(1241))/2*8x2 = (-21 - sqrt(1241))/2*8   S = {(x1,x2)}  (S inseamna solutia)