Question

Folosind fomulele de calcul prescurtat, sa se calculeze:
a) $( \sqrt{5} -2) ^{2}$
b) $( \sqrt[3]{2} - \sqrt{5} ) ^{2}$
c) $(1+ \sqrt{2} + x^{3} ) ^{2}$
d) $( \sqrt{12} - \sqrt{7} ) (\sqrt{12} - \sqrt{7} )$
e) $(2+ \sqrt{3} - \sqrt{2} )(2+ \sqrt{3} + \sqrt{2} )$

Answer 1

a) (√5-2)²=√5²-2√5·2+2²=5-4√5+4=9-4√5
b) (∛2-√5)²=∛2²-2∛2·√5+√5²=∛4-2∛2·√5+5
c)(1+√2+x³)²=1²+√2²+(x³)²+2·1·√2+2·1·x³+2·√2·x³=1+2+x⁶+2√2+2x³+2√2x³= 
=3+2√2+2·(1+√2)x³+x⁶
d) (√12-√7)·(√12-√7)=(√12-√7)²=√12²-2·√12·√7+√7²=12-2·2√3·√7+7=19-4√21
e) (2+√3-√2)(2+√3+√2)=[(2+√3)-√2][(2+√3)+√2]=(2+√3)²-√2²=2²+2·2·√3+√3²-2=
=4+4√3+3-2=5+4√3