Question

Срочно!!! Показникові рівняння!

Answer 1

$(2 {}^{x - 6} ) {}^{x - 3} = \dfrac{1}{4} \\ 2 {}^{(x - 6)(x - 3)} = 2 {}^{ - 2} \\ 2 {}^{x {}^{2} - 9x + 18 } = 2 {}^{ - 2} \\ x {}^{2} - 9x + 18 = - 2 \\ x {}^{2} - 9x + 18 + 2 = 0 \\ x {}^{2} - 9x + 20 = 0$

D=(-9)²-4*1*20=81-80=1; √D=√1=1

$x _{1} = \dfrac{9 - 1}{2} = \dfrac{8}{2} = 4 \\ x_{2} = \dfrac{9 + 1}{2} = \dfrac{10}{2} = 5$