Решите уравнение и неравенство.. Created by kuban5. algebra-ru

Решите уравнение и неравенство...

July 2022 1 3 Report

Решите уравнение и неравенство.

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m11m 4^x -9*2^x=-14
Пусть 2^x=y

y² -9y=-14
y² -9y+14=0
D=81-56=25
y₁=9-5=2
2
y₂=9+5=7
2

При у=2
2^x=2
x=1

При у=7
2^x=7
x=log₂ 7

Ответ: 1; log₂ 7.

3x²+8x-3 ≥0
(5^x)-25

{(5^x)-25≠0
{(3x²+8x-3)((5^x)-25)≥0

(5^x) -25≠0
(5^x)≠5²
x≠2

(3x²+8x-3)((5^x)-25)≥0
Разложим 3x²+8x-3 на множители:
3x²+8x-3=0
D=64+4*3*3=64+36=100
x₁=-8-10=-3
6
x₂=-8+10=1/3
6
3x²+8x-3=3(x+3)(x-1/3)

3(x+3)(x-1/3)((5^x)-25)≥0
x=-3 x=1/3 x=2
- + - +
--------- -3 -------------- 1/3 -------------- 2 ---------------
\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\
x∈[-3; 1/3] U (2; +∞)

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