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popovaviktoriy3
@popovaviktoriy3
July 2022
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решите,пожалуйста (10 класс)
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sharadi
Verified answer
Все неравенства решаем вынесением общего множителя за скобки.
а)2ˣ(2² +1) > 20
2ˣ*5 > 20
2ˣ > 4
2ˣ > 2²
x>2
б) 3ˣ(3² -1 )<24
3ˣ * 8 < 24
3ˣ < 3
x < 1
в) 4ˣ(4 +1) > 1,25
4ˣ *5 > 5/4
4ˣ > 1/4
4ˣ > 4⁻¹
x > -1
г) 3²ˣ(3 - 1) < 2/3
3²ˣ * 2 < 2/3
3²ˣ< 1/3
3²ˣ < 3⁻¹
2x < -1
x < -1/2
д) 4ˣ⁻¹(4 -1) < 3
4ˣ⁻¹ * 3 < 3
4ˣ⁻¹ < 1
4ˣ⁻¹ < 4⁰
x -1 < 0
x < 1
е) 5ˣ⁻²(5² -1) <24
5ˣ⁻² * 24 < 24
5ˣ⁻² < 1
5ˣ⁻² < 5⁰
x -2 < 0
x < 2
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Answers & Comments
Verified answer
Все неравенства решаем вынесением общего множителя за скобки.а)2ˣ(2² +1) > 20
2ˣ*5 > 20
2ˣ > 4
2ˣ > 2²
x>2
б) 3ˣ(3² -1 )<24
3ˣ * 8 < 24
3ˣ < 3
x < 1
в) 4ˣ(4 +1) > 1,25
4ˣ *5 > 5/4
4ˣ > 1/4
4ˣ > 4⁻¹
x > -1
г) 3²ˣ(3 - 1) < 2/3
3²ˣ * 2 < 2/3
3²ˣ< 1/3
3²ˣ < 3⁻¹
2x < -1
x < -1/2
д) 4ˣ⁻¹(4 -1) < 3
4ˣ⁻¹ * 3 < 3
4ˣ⁻¹ < 1
4ˣ⁻¹ < 4⁰
x -1 < 0
x < 1
е) 5ˣ⁻²(5² -1) <24
5ˣ⁻² * 24 < 24
5ˣ⁻² < 1
5ˣ⁻² < 5⁰
x -2 < 0
x < 2