Question

Помогите дам 100 ПЖ ​

Answer 1

Ответ:

Объяснение:

$\displaystyle\bf\\2^{x^2+x-6}-2^{x^2+x-9}=56\\\\2^{x^2+x-9}(2^3-1)=7\cdot8\\\\2^{x^2+x-9}\cdot7=7\cdot8\\\\2^{x^2+x-9}=2^3\\\\x^2+x-9=3\\\\x^2+x-12=0\\\\po~Vieta~~x=-4;x=3\\\\Otvet:-4;3$

Answer 2

$2 {}^{x {}^{2} + x - 6} - 2 {}^{x {}^{2} + x - 9} = 56. \\ 2 {}^{x {}^{2} + x} \times 2 {}^{ - 6} - 2 {}^{x {}^{2} + x } \times 2 {}^{ - 9} = 56. \\ 2 {}^{x {}^{2} + 2} \times \frac{1}{2 {}^{6} } - 2 {}^{x {}^{2} + x} \times \frac{1}{2 {}^{9} } = 56. \\ 2 {}^{x {}^{2} + x} \times \frac{1}{64} - 2 {}^{x {}^{2} + x} \times \frac{1}{512} = 56. \\ \bigg( \frac{1}{64} - \frac{1}{512} \bigg) \times 2 {}^{x {}^{2} + x } = 56. \\ \bigg( \frac{8 - 1}{512} \bigg) \times 2 {}^{x {}^{2} + x} = 56. \\ \frac{7}{512} \times 2 {}^{x {}^{2} + x } = 56 \: \: \: \: \: | \times \frac{512}{7} \to \\ 2 {}^{x {}^{2} + x } = 4096. \\ 2 {}^{x {}^{2} + x } = 2 {}^{12} . \\ x {}^{2} + x = 12. \\ x {}^{2} + x - 12 = 0. \\ d = 1 {}^{2} - 4 \times 1 \times ( - 12) = 1 + 48 = 49 = 7 {}^{2} . \\ x_{1} = \frac{ - 1 - 7}{2} = \frac{ - 8}{2} = - 4. \\ x_{2} = \frac{ - 1 + 7}{2} = \frac{6}{2} = 3.$