Question

Если a-(1/5)=0,5 то, (a^2+(1/a^2))^0.5 =?

Answer 1

$a-frac{1}{a}=0,5\\(a-frac{1}{a}){2}=0,5^{2} \\a^{2} -2*a*frac{1}{a} +frac{1}{a^{2}} =0,25\\a^{2}-2+frac{1}{a^{2}}=0,25\\a^{2}+frac{1}{a^{2}}=2,25\\\(a^{2}+frac{1}{a^{2}} )^{0,5} =2,25^{0,5}\\(a^{2}+frac{1}{a^{2}})^{0,5}=sqrt{2,25}\\(a^{2}+frac{1}{a^{2}} )^{0,5}=1,5$