Question

Stiind ca a + 1/a=5/2, unde a este numar real, aratati ca a^2+1a^2=17/4

Answer 1

[tex]a + \frac{1}{a}= \frac{5}{2} \\

(a+ \frac{1}{a})^{2}= a^{2} + 2*a*\frac{1}{a}+\frac{1}{a^{2}}= a^{2} + 2 + \frac{1}{a^{2}}\\ \\ \\ \\ (a + \frac{1}{a})^{2 }=( a^{2} + 2 + \frac{1}{a^{2}})/ (-2)\\ \\ (a + \frac{1}{a})^{2} -2 = a^{2} + \frac{1}{a^{2}} \\ \\ \\

a^{2} + \frac{1}{a^{2}} = (a+\frac{1}{a})^{2} -2 =( \frac{5}{2} )^{2} -2 = \frac {25}{4} -2 = \frac{25}{4} - \frac{8}{4} = \frac{25-8}{4} = \frac{17}{4}

[/tex]

Answer 2

Salut,

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


Succes! :3