Algebra - rovnice
Prosím o pomoc s těmito rovnicemi.
Odpovědi
Diskuze
log2(x) - log2(√x) - log2(1/x) = -1
log2(x) - 1/2 * log2(x) - log2(1/x) = -1
log2(x)*(1 - 1/2) - log2(1/x) = -1
log2(x)*(1/2) - log2(1/x) = -1
log2(x)*(1/2) - log2(1/x) = -1
log2(√x) - log2(1/x) = -1
log2(√x / x) = -1
log2(1 / √x) = -1
(1 / √x) = 2^-1 = 1/2
√x = 2
x = 4
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b) 7^(x+2) + 2*7^(x-1) = 345
7^(x+2) + 2*7^(x-1) = 345
1 + 2*7^(x-1) / 7^(x+2) = 345 / 7^(x+2)
1 + 2*7^(x-1 - (x+2) ) = 345 / 7^(x+2)
1 + 2*7^(-3) = 345 / 7^(x+2)
1 + 2/343 = 345 / 7^(x+2)
345/343 = 345 / 7^(x+2)
343 = 7^(x+2)
343 = 7^(x+2)
7*7*7 = 7^(x+2)
7^3 = 7^(x+2)
3 = x+2
x=1
===
c) sin(x) - sin(2x) = 0
https://people.ksp.sk/~morgoth/tahaky_v2.pdf
sin 2x = 2 sin x * cos x
sin(x) - sin(2x) = 0
sin(x) - 2*sin(x)*cos(x) = 0
sin(x) * ( 1 - 2*cos(x) ) = 0
sin(x)=0
x=0
x1=0
====
1 - 2*cos(x) = 0
1 = 2*cos(x)
1/2 = cos(x)
x = arccos(1/2) = 60°
x2=60°
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