Question

calculati folosind formulele de calcul prescurtat a) (2+√2)^2-(2√2-3)^2 b) (√3+2)^2 c) (√3-1)^2 +(2√3+1)^2 d) (2√3-1)^2-(2√2-1)(2√2-1)(2√2+1)

Answer 1

a)  = [(2+√2)-(2√2-3)]*[(2+√2)+(2√2-3)]=(2+√2-2√2-3)*(2+√2+2√2-3)=(2-√2-3)*(2+3√2-3)=(-1-√2)(-1+3√2)=1+√2-3√2-3*2=1+√2-3√2-6=-5-2√2
b)=3+2*2*√3+4=3+4√3+4=7+4√3
c)=(3-2√3+1)+(12+4√3+1)=(4-2√3)+(13+4√3)=4-2√3+13+4√3=17+2√3
d)=(2√3-1)²-(2√2-1)[(2√2)²-1²]=12-4√3+1-(2√2-1)*(8-1)=13-4√3+14√2+7=20-4√3+14√2