Question

Va rooog sa ma ajutatiii!Multumesc frumos!
Efectuati:
$a)( \frac{5}{2 \sqrt{2}+ \sqrt{3} } - \frac{2}{ \sqrt{5}+ \sqrt{3} } + \frac{18}{ 2\sqrt{5}- \sqrt{2} } - \frac{3}{ \sqrt{5}-2 \sqrt{2} })* \frac{ \sqrt{10} }{ \sqrt{5}+ \sqrt{2} }.$

Answer 1

[5(2√2-√3)/5  -2(√5-√3)/2  +18(2√5+√2)/18 + 3(√5+2√2)/3]*√10(√5-√2)/3
simplificand avem
[(2√2-√3)-(√5-√3)+(2√5+√2)+(√5+2√2)]*(5√2-2√5)/3=
(2√2-√3-√5+√3+2√5+√2+√5+2√2)*(5√2-2√5)/3=
(5√2+2√5)*(5√2-2√5)/3=
conform formulei
(a+b)(a-b)=a²-b²
avem
=[(5√2)²-(2√5)²]/3=(50-20)/3=30:3=10