Question

Efectuati calculele:
a) $\frac{1}{ \sqrt{2}+1 }+ \frac{1}{ \sqrt{3}+ \sqrt{2} } + \frac{1}{ \sqrt{5}+ \sqrt{4} } + \frac{1}{ \sqrt{4}+ \sqrt{3} }=$

b) $\frac{9}{ \sqrt{18} }- \frac{9}{ \sqrt{8}} + \frac{9}{6 \sqrt{2} } - \frac{9}{6 \sqrt{8} }=$

Answer 1

1)(√2-1)/(2-1) + (√3-√2)/(3-2) + (√5-√4)/(5-4) + (√4-√3)/(4-3)=

√2 -1 + √3 -√2 +√5 -2 +2 -√3=

= -1 +√5

2)9√18/18  -9√8/8 +9√2/12 -9√8/6*8=

=3√2/2 -9√2/4 + 3√2/4 -3√2/8    aducem la acelasi numitor

= (12√2 - 18√2 + 6√2 -3√2)/8=

=(18√2 -21√2)/8=  -3√2/8