Question

9. efectuati calculele
a) 4/radical2-1 +5/radical 2+1 - 7/ 3-radical 2
b ) 2/ 2 radical 7-5 + 11/ 3 radical 2 - radical 7 - 5/ radical 7 - radical 2
c) 1/ radical 2 +1 +1/radical 3 +radical 2 + 1/ radical 4 + radical 3 + 1 /radical 5 + radical 4
d ) (1/ radical 6 +radical 5 + 1/ radical 7 + radical 6 + 1/ radical 8 +radical 7 + 1/ radical 9 + radical 8 ) x 1 /3 - radical 5
va rog !

Answer 1

se rationalizeaza fractiile
a) 4/(√2-1) +5/(√2+1) - 7/(3-√2 )=
=4(√2+1)/(√2-1)(√2+1) +5(√2-1)/(√2+1)(√2-1) - 7(3+√2)/(3-√2 )(3+√2)=
=4(√2+1)/(2-1) +5(√2-1)/(2-1) - 7(3+√2)/(9-2 )=
=4(√2+1) +5(√2-1) - 7(3+√2)/7=
=4√2+4 +5√2-5 - 3-√2=
=8√2-4


b ) 2/ (2√7-5) + 11/(3√2 - √7) - 5/(√7 -√2)=
=2(2√7+5)/ (28-25) + 11(3√2+√7)/(18 - 7) - 5(√7 +√2)/(7 -2)=
=(4√7+10)/3 + 3√2+√7 - √7 -√2=
=(4√7+10)/3 + 2√2=
=(4√7+10+6√2)/3

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


 d ) (1/(√6 +√5) + 1/(√7 + √6) + 1/( √8 +√7) + 1/( √9 + √8 ) x 1 /(3 - √5) =
=[(√6-√5) /(6-5)+(√7-√6)/(7-6) + (√8-√7)/(8-7) + (3-√8 )/(9-8)] x (3+√5)/(9-5) =
=(√6-√5+√7-√6 + √8-√7 +3-√8 ) x (3+√5)/4 =
=(3-√5 ) x (3+√5)/4 =
=(9-5)/4 =4/4=1