Question

4 elevado a X + 4 elevado a -X = 5÷2​

Answer 1

Resposta:

X'=1/2

X"=-1/2

Explicação passo-a-passo:

(4^x) + 4^(-x)=5/2

(4^x)/1 + 1/(4^x) = 5/2

(4^x)²+1/(4^x) = 5/2

4^x=t

(t²+1)/t = 5/2

2(t²+1)=5t

2t²+2-5t=0

2t²-5t+2=0

Δ=(-5)²-4.2.2

Δ=25-16

Δ=9

T=-(-5)±√(9)/2.2

T=5±3/4

T'=5+3/4

T'=8/4

T'=2

T"=5-3/4

T"=2/4

T"=1/2

4^x=T

4^x'=T'

4^x'=2

2^(2x')=2^(1)

2x'=1

X'=1/2

4^x"=T"

4^x"=1/2

2^(2x") = 2^(-1)

2x"=-1

X"=-1/2