Question

2^(10x^2-8x-23)+2^(5x^2-4x-12)-3=0

Answer 1

2^(10x^2-8x-23)+2^(5x^2-4x-12)-3=0

2^(10x^2-8x-24+1)+2^(5x^2-4x-12)-3=0

2*2^(10x^2-8x-24)+2^(5x^2-4x-12)-3=0

2^(5x^2-4x-12) = a > 0

2a^2 + a - 3 = 0

D = 1 - 4*(-3)*2 = 25

a12 = (-1 +- 5)/4 = 1     - 3/2

a1 = -3/2 < 0 нет

a2 = 1

2^(5x^2-4x-12) = 1

2^(5x^2-4x-12)=2^0

5x^2-4x-12 = 0

D = 16 + 4*5*12 = 256 = 16^2

x12 = (4 +- 16)/10 = 2    -6/5

ответ х = {-6/5, 2}