Question

Calculati:

$( \sqrt{3} + \sqrt{5}x )^{2} - ( \sqrt{15} x - 2)^{2}$
$(3 - \sqrt{14} x )^{2} - ( \sqrt{7} x + \sqrt{2} )^{2}$
$(2 \sqrt{2}x - \sqrt{3} )^{2} + ( \sqrt{2} + 2 \sqrt{3} x)^{2}$
$( \sqrt{5} x + 4 \sqrt{2} )^{2} - (3 \sqrt{2} x - \sqrt{5} )^{2}$


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Answer 1

Răspuns:

Explicație pas cu pas:

a) (√3 + √5·x)²-(√15·x-2)²=(√3)²+2·√3·√5·x+(√5·x)² - [(√15·x)²-2·√15·x·2+2²] = 3+2·√15·x+5x²-(15x²-4√15·x+4)=3+2·√15·x+5x²-15x²+4√15·x-4=

=-10x²+6√15·x-1;

b) ... = 3²-2·3·√14·x+(√14·x)² - [(√7·x)²+2·√7·x·√2+(√2)²]=9-6√14·x+14x² -7x²-2√14·x-2=7x²-8√14·x+7;

c) ... = (2√2·x)²-2·2√2·x·√3+(√3)²+(√2)²+2·√2·2√3·x+(2√3·x)²=

=8x²-4√6·x+3+2+4√6·x+12x²=20x²+5;

d) ... = (√5·x)²+2·√5·x·4√2+(4√2)²-[(3√2·x)²-2·3√2·x·√5+(√5)²]=

=5x²+8√10·x+32-(18x²-6√10·x+5)=5x²+8√10·x+32-18x²+6√10·x-5=

= -13x²+14√10·x+27.