Question

Determinati x si y nrumera naturale astfel incat y la puterea x +2 la puterea y =65

Answer 1

y^x+2^y=65
y^x+2^6=65
6^⁰+64=65

y=6
x=0

Answer 2

$(y^{x+2}) ^y} = 65 \\ y^{y(x+2)}= 65^{1} \\ y=65 \\ y(x+2) = 1 \\ 65(x+2) = 1 \\ x+2 = \frac{1}{65} \\ x = \frac{1}{65}-2 \\ \\ x= \frac{1-130}{65} \\ \\ x = -\frac{129}{65}$

Deci: x = -129/65.    y = 65.