Question

REZOLVATI IN R ECUATIILE:
a) $\frac{X-3}{1} + \frac{X-3}{2} +....+ \frac{X-3}{2014} =0$
b)$\frac{X-2}{2} + \frac{X-2}{6} + \frac{X-2}{12} +....+ \frac{X-2}{2014*2015} =2014$
c)$\sqrt{(6- \sqrt{5}) ^{2} } + \sqrt{41+12 \sqrt{5} } *x= \sqrt{(6- \sqrt{5}) ^{2} } *x- \sqrt{41-12 \sqrt{5} }$
va rogg ajutati-ma
dau coroana

Answer 1

Observăm că :

$\it 41\pm12\sqrt5 = ( 6\pm\sqrt5)^2$

Ecuația devine:


$\it c)\ \sqrt{(6-\sqrt5)^2} +\sqrt{(6+\sqrt5)^2} x =\sqrt{(6-\sqrt5)^2} x - \sqrt{(6-\sqrt5)^2}$

$\it \Leftrightarrow 6-\sqrt5 +(6+\sqrt5)x =(6-\sqrt5)x - (6-\sqrt5)\Leftrightarrow$

$\it \Leftrightarrow (6+\sqrt5-6+\sqrt5)x = -(6-\sqrt5) - (6-\sqrt5) \Leftrightarrow$

$\it \Leftrightarrow 2\sqrt5 x = \sqrt5-6+\sqrt5-6 \Leftrightarrow 2\sqrt5 x = 2(\sqrt5-6)|_{:2} \Leftrightarrow$

$\it \Leftrightarrow \sqrt5 x = \sqrt5-6 \Leftrightarrow x = \dfrac{^{\sqrt5)}\sqrt5-6} {\ \sqrt5} \Leftrightarrow x = \dfrac{5 - 6\sqrt5}{5}.$