Question

Arătați că:
(1+0,5)(1-0,5)+($\frac{1}{ \sqrt{2} } )^{2}$=$\frac{5}{4}$

Answer 1

$(1+0,5)(1-0,5)+\Big(\frac{1}{\sqrt{2}}\Big)\Up^2=$
$1,5\cdot0,5+\frac{1}{2}=$
$0,75+0,5=1,25=\frac{5}{4}$

Answer 2

[tex]0,5 = \frac{1}{2} \\\\ 1 = \frac{1}{1} = \frac{2}{2}[/tex]

Așadar, putem rescrie, ducând și puterea la numărător, respectiv numitor:

[tex](1+\frac{1}{2})(1-\frac{1}{2}) + \frac{1^2} {{\sqrt 2} ^ 2} = \\\\ (\frac{2}{2}+\frac{1}{2})(\frac{2}{2}-\frac{1}{2}) + \frac{1} {2} = \\\\ \frac{3}{2} * \frac{1}{2} + \frac{1} {2} = \\\\ \frac{3}{4} + \frac{1} {2} = \\\\ \frac{3}{4} + \frac{2} {4} = \\\\ \frac{2+3} {4} = \frac{5} {4}[/tex]