1) 2^x=1+2x-x^2 2) (x^2-7x+13)^x-7 1 3) y=7^x-4, -4 - id580272420220113 от Светасветасветасвета 13.01.2022 03:35

Question

Алгебра: 1) 2^x=1+2x-x^2 2) (x^2-7x+13)^x-7 1 3) y=7^x-4, -4

Светасветасветасвета · Accepted Answer

(2sin x - √2)(2cosx + 1) = 0⇒
1) 2sin x - √2=0⇒2sin x=√2⇒sinx=√2/2⇒
x=π/4+2πn; x=3π/4+2πn
n=0⇒x=π/4∈[-π;π]; x=3π/4∈[-π;π]
n=1⇒x=π/4+2π=9π/4∉[-π;π]; x=3π/4+2π=11/4∉[-π;π]
n=-1⇒x=π/4-2π=-3π/4∈[-π;π]; x=3π/4-2π=-π/4∈[-π;π]
n=-2⇒x=π/4-4π=-15π/4∉[-π;π]; x=3π/4-4π=-13/4∉[-π;π]
2) 2cosx + 1=0⇒2cos x=-1⇒cosx=-1/2⇒
x=2π/3+2πn; x=-2π/3+2πn
n=0⇒x=2π/3∈[-π;π]; x=-2π/3∈[-π;π]
n=1⇒x=2π/3+2π=8π/3∉[-π;π]; x=-2π/3+2π=8/3∉[-π;π]
n=-1⇒x=2π/3-2π=-4π/3∉[-π;π]; x=-2π/3-2π=-8π/3∉[-π;π]
ответ:
x=π/4; x=3π/4
x=-3π/4; x=-π/4
x=2π/3; x=-2π/3

1) 2^x=1+2x-x^2 2) (x^2-7x+13)^x-7> 1 3) y=7^x-4, -4

MOGZ ответил