rożwiąże ktoś ? ;d .Ale, zeby było poprawnie ;d . DAM NAJ ! .... Question from @Viciusia112

Viciusia112 @Viciusia112

November 2018 1 28 Report

rożwiąże ktoś ? ;d .

Ale, zeby było poprawnie ;d .

DAM NAJ ! .

valletka

Zadanie 2.

$a)\ 2*(3+x)^2-(2-x)^2-3*(2-x)(2+x)=\\2*(9+6x+x^2)-(4-4x+x^2)-3*(4-x^2)=\\18+12x+2x^2-4+4x-x^2-12+3x^2=\\4x^2+16x+6$

$b)\ (4x-3y)(4x+3y)-2*(4x+3y)^2+2*(3x-4y)^2=\\16x^2-9y^2-2*(16x^2+24xy+9y^2)+2*(9x^2-24xy+16y^2)=\\16x^2-9y^2-32x^2-48xy-18y^2+18x^2-48xy+32y^2=\\2x^2-96xy+5y^2$

$c)\ (x+2)^2-(3x+2)(3x-2)-(\sqrt{3}+x)^2=\\x^2+4x+4-(9x^2-4)-(3+2x\sqrt{3}+x^2)=\\x^2+4x+4-9x^2+4-3-2x\sqrt{3}-x^2=\\-9x^2+4x-2x\sqrt{3}+5=\\-9x^2+2x(2-\sqrt{3})+5$

$d)\ (x-3)^2+\sqrt{5}*(2x+\sqrt{5})(\sqrt{5}-2x)-(1-x)^2=\\x^2-6x+9+\sqrt{5}*(2x\sqrt{5}-4x^2+5-2x\sqrt{5})-(1-2x+x^2)=\\x^2-6x+9+\sqrt{5}*(-4x^2+5)-1+2x-x^2=\\x^2-6x+9-4x^2\sqrt{5}+5\sqrt{5}-1+2x-x^2=\\-4x^2\sqrt{5}-4x+8=-4(x^2\sqrt{5}+x-2)$

Zadanie 3.

$a)\ \frac{3}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}=\frac{3\sqrt{3}-3}{3-1}=\frac{3\sqrt{3}-3}{2}$

$b)\ \frac{2\sqrt{5}}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{2\sqrt{15}-2\sqrt{5}}{3+1}=\frac{2\sqrt{15}-2\sqrt{5}}{4}=\frac{2(\sqrt{15}-\sqrt{5})}{4}=\frac{\sqrt{15}-\sqrt{5}}{2}$

$c)\ \frac{4}{2\sqrt{3}+3}*\frac{2\sqrt{3}-3}{2\sqrt{3}-3}=\frac{8\sqrt{3}-12}{12-9}=\frac{8\sqrt{3}-12}{3}$

$d)\ \frac{\sqrt{2}}{2\sqrt{3}-3}*\frac{2\sqrt{3}+3}{2\sqrt{3}+3}=\frac{2\sqrt{6}+3\sqrt{2}}{12-9}=\frac{2\sqrt{6}+3\sqrt{2}}{3}$

$e)\ \frac{2-3\sqrt{2}}{2\sqrt{3}-2}*\frac{2\sqrt{3}+2}{2\sqrt{3}+2}=\frac{4\sqrt{3}+4-6\sqrt{6}-6\sqrt{2}}{12-4}=\frac{2(2\sqrt{3}+2-3\sqrt{6}-3\sqrt{2})}{8}=\\ \frac{2\sqrt{3}+2-3\sqrt{6}-3\sqrt{2}}{4}$

$f)\ \frac{\sqrt{5}+2}{\sqrt{3}-3\sqrt{2}}*\frac{\sqrt{3}+3\sqrt{2}}{\sqrt{3}+3\sqrt{2}}=\frac{\sqrt{15}+3\sqrt{10}+2\sqrt{3}+6\sqrt{2}}{3-18}=\frac{\sqrt{15}+3\sqrt{10}+2\sqrt{3}+6\sqrt{2}}{-15}$

$g)\frac{3-\sqrt{2}}{\sqrt{3}-2}*\frac{\sqrt{3}+2}{\sqrt{3}+2}=\frac{3\sqrt{3}+6-\sqrt{6}-2\sqrt{2}}{3-4}=\frac{3\sqrt{3}+6-\sqrt{6}-2\sqrt{2}}{-1}=\\-(3\sqrt{3}+6-\sqrt{6}-2\sqrt{2})=-3\sqrt{3}-6+\sqrt{6}+2\sqrt{2}$