Question

Stiind ca "a" la partat +( 1 supra "a" la partat) = 15 , sa se calculeze a+(1 supra a)

Answer 1

[tex]\left(a+\dfrac{1}{a}\right)^2=a^2+2a\cdot\dfrac{1}{a}+ \left(\dfrac{1}{a} \right)^2=a^2+2+\dfrac{1}{\ a^2} =15+2=17 \\\;\\ \left(a+\dfrac{1}{a}\right)^2= 17 \Longrightarrow \sqrt{\left(a+\dfrac{1}{a}\right)^2}= \sqrt{17} \Longrightarrow \left|a+\dfrac{1}{a}\right| =\sqrt{17} \\\;\\ \Longrightarrow a+\dfrac{1}{a}= \pm\sqrt{17} \\\;\\ . [/tex]