Wskaż, że podane liczby są liczbami całkowitymi:
a) 1/(√2-1)-√2
b) (√3-2)/(√3+2)-12/√3
c) 1/(3+√6)+1/(3-√6)
d) (√7+√5)/(√7-√5)+(√7-√5)/(√7+√5)
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a)
1/(√2-1)-√2=(√2-1)/(2-1)-√2=-1
b) (√3-2)/(√3+2)-12/√3= ((√3-2)(√3-2))/((√3+2)(√3-2))-(12√3)/3=(3-2√3-2√3+4)/(3-4)-4√3=-(7-4√3)-4√3=-7+4√3-4√3=-7
c) 1/(3+√6)+1/(3-√6) =((3-√6))/((3+√6)(3-√6))+((3+√6))/((3-√6)(3+√6))=(3-√6+√6+3)/(9-6)=2
d) (√7+√5)/(√7-√5)+(√7-√5)/(√7+√5)= ((√7+√5)(√7+√5))/((√7-√5)(√7+√5))+((√7-√5)(√7-√5))/((√7+√5)(√7-√5))=(7+√35+√35+5+7-√35-√35+5)/(7-5)=24/2=12
rozw w zał.