Question

решите уровнение
9^(x^2-3)=3^(3*x-7)

Answer 1

${9}^{ {x}^{2} - 3 } = {3}^{3x - 7 } \\ {3}^{2( {x}^{2} - 3) } = {3}^{3x - 7 } \\ 2 {x}^{2} - 6 = 3x - 7 \\ 2 {x}^{2} - 3x + 1 = 0 \\ d = 9 - 8 = 1 \\ x = \frac{3 + 1}{4} = 1 \\ x = \frac{3 - 1}{4} = \frac{2}{4} = \frac{1}{2}$
Ответ : х=1;0,5

Answer 2

9^(x²-3)=3^(3x-7) ;x€R
3^(2x²-6)=3^(3x-7)
2x²-6=3x-7
2x²-3x+1=0
D=9-8=1
x=(3±1)/4
x1=1;x2=1/2