Question

Va rog! Pls!
a^43+b^47=4^1011 Dati exemple de a si b.

Answer 1

Răspuns:

a=2^47

b=2^43

Explicație pas cu pas:

"se observa" ca 43*47=2021

(45-2) (45+2) =45²-2²=2025-4=2021

si ca 2^2022=2*2^2021

4^1011=2^2022=2*2^2021=2^2021+2^2021= (2^47)^43+(2^43)^47

a=2^47

b=2^43

Answer 2

$\it 4^{1011}=(2^2)^{1011}=2^{2022}=2^{1+2021}=2\cdot2^{2021}=2^{2021}+2^{2021}=\\ \\ =2^{47\cdot43}+2^{43\cdot47}=(2^{47)^{43}}+(2^{43})^{47}\\ \\ Deci,\ (2^{47)^{43}}+(2^{43})^{47}=4^{1011},\ prin\ urmare:\ a=2^{47},\ \ b=2^{43}$