Question

Efectuați cu formulele de calcul prescurtat următoarele :
(2√3+x)²=
(3√3x+2√5)²=
(½x+3)²=
(3-2√3)²=

Answer 1

$a).(2 \sqrt{3} +x)^2=(2 \sqrt{3} )^2+2*2 \sqrt{3} *x+x^2=12+4x \sqrt{3} +x^2 \\ \\ b).(3 \sqrt{3} x+2 \sqrt{5} )^2=(3 \sqrt{3} x)^2+2*3 \sqrt{3} x*2 \sqrt{5} +(2 \sqrt{5} )^2= \\ \\ =27x^2+12 \sqrt{15} +20 \\ \\ c).( \frac{1}{2} x+3)^2=( \frac{1}{2} x)^2+2* \frac{1}{2} x*3+3^2= \frac{1}{4} x^2+3x+9 \\ \\ d).(3-2 \sqrt{3} )^2=3^2-2*3*2 \sqrt{3} +(2 \sqrt{3} )^2=9-12 \sqrt{3} +12= \\ \\ =21-12 \sqrt{3}$