Question

1.Stiind ca a+ $\frac{1}{a}$ = $\frac{5}{2}$ , unde a este numar real nenul , aratati ca a² + $\frac{1}{ a^{2} }$ = $\frac{17}{ 4 }$
2.Stiind ca x+ $\frac{1}{x}$ =-2 , unde x este numar real nenul ,aratati ca x²+ $\frac{1}{ x^{2} }$=2

Answer 1

1.
a+1/a=5/2  ridicam la puterea 2
(a+1/a)²=(5/2)²
a²+2×a×1/a+1/a²=25/4
a²+2+1/a²=25/4
a²+1/a²=25/4-2
a²+1/a²=(25-2×4)/4
a²+1/a²=(25-8)/4
a²+1/a²=17/4


2.
x+1/x=-2  ridicam la puterea 2
(x+1/x)²=(-2)²
x²+2x×1/x+1/x²=4
x²+2+1/x²=4
x²+1/x²=4-2
x²+1/x²=2