Question

Dane są liczby

x=3+2√7 ,y=5-3√7

oblicz:x+y, x-y,xy ,x², x/y ,y²

Answer 1

x+y= 3+2√7 +5-3√7=8-√7

x-y= 3+2√7 -(5-3√7)= 3+2√7 -5+3√7= -2+5√7

x*y= (3+2√7)(5-3√7)= 15-9√7+10√7-6√7= 15-5√7

x²= (3+2√7)²= 9+12√7+28= 12√7+37

x/y=  (3+2√7)/(5-3√7)= 3+2√7 * 5+3√7/5+3√7= (3+2√7)(5+3√7)/25-63=15+9√7+10√7+6√7/-38=15+25√7/-38

y²=(5-3√7)²=25-30√7+42=67-30√7