Enačba

Mi lahko nekdo pomaga, kako rešiti to enačbo: 16 ^ ((sqrt(5) +3)/(sqrt(5) -2 )) / 64^ ((50+23sqrt(5) ) / (sqrt(45)) )?

Racionaliziraš ulomka v eksponentih:

(sqrt(5)+3)/(sqrt(5)-2 ) = (sqrt(5)+3)(sqrt(5)+3)/(sqrt(5)+2)/(sqrt(5)-2)(sqrt(5)+2) = 11+5 sqrt(5)
(50+23sqrt(5))/(sqrt(45)) = (50+23sqrt(5))/(3sqrt(5))=(50sqrt(5)+23*5)/(3*5) = (10sqrt(5)+23)/3

Potem upoštevaš, da je 16=2^4 in 64=2^6:

16^(11+5 sqrt(5)) = 2^4(11+5 sqrt(5)) = 2^(44+20sqrt(5))
64^((10sqrt(5)+23)/3) = 2^6((10sqrt(5)+23)/3) = 2^2(10sqrt(5)+23) = 2^(20sqrt(5)+46)

Finale:

[2^(44+20sqrt(5))]/[2^(20sqrt(5)+46)] = 2^[(44+20sqrt(5)) - (20sqrt(5)+46)] = 2^(-2) = 1/4

povezave med osnovama 3 in 5 zagotovo ni. 4^sqrt(3) = (2²)^sqrt(3) = 2^2*sqrt(3)

Ja no, sej ti je že gor napisal, da je rezultat 1/4. osnovo 16 izraziš kot 2⁴ in 64 kot 2⁶. 0.25 pa je isto kot 1/4.