Cześć ;-)
Obliczenia do a]
[tex]x=0,01^{0,5}=0,01^{\frac{5}{10}}=0,01^{\frac{1}{2}}=\sqrt{0,01}=0,1\\\\\text{zatem}:\\\\(-x+2)(4-3x)=-4x+3x^2+8-6x=\\\\=3x^2-10x+8=3\cdot0,1^2-10\cdot0,1+8=\\\\=3\cdot0,01-1+8=0,03+7=7,03[/tex]
Obliczenia do b]
[tex]a=\sqrt2-1\\\\\text{zatem}\\\\(2a+1)(a^2-a-1)-2(a^2+1)(a-1)=\\\\=2a^3-2a^2-2a+a^2-a-1-2(a^3-a^2+a-1)=\\\\=2a^3-2a^2-2a+a^2-a-1-2a^3+2a^2-2a+2=\\\\=a^2-5a+1=(\sqrt2-1)^2-5(\sqrt2-1)+1=\\\\=(\sqrt2)^2-2\cdot\sqrt2\cdot1+1^2-5\sqrt2+5+1=\\\\=2-2\sqrt2+1-5\sqrt2+5+1=9-7\sqrt2[/tex]
Obliczenia do c]
[tex]x=16^{0,3}:16^{0,05}=16^{0,3-0,05}=16^{0,25}=16^{\frac{1}{4}}=\sqrt[4]{16}=2\\\\\text{zatem}\\\\(2x-3)^2-(2x+3)^2+4x=(2x)^2-2\cdot2x\cdot3-((2x)^2+2\cdot2x\cdot3+3^2)+4x=\\\\=4x^2-12x+9-(4x^2+12x+9)+4x=4x^2-12x+9-4x^2-12x-9+4x=\\\\=-20x=-20\cdot2=-40[/tex]
Obliczenia do d]
[tex]x=-2\sqrt[4]9\\\\\text{zatem}\\\\(x-1)^2(x+1)^2-(x^2+1)^2=(x^2-2x+1)(x^2+2x+1)-(x^4+2x^2+1)=\\\\=x^4+2x^3+x^2-2x^3-4x^2-2x+x^2+2x+1-x^4-2x^2-1=\\\\=-4x^2=-4\cdot(-2\sqrt[4]9)^2=-4\cdot(-2)^2\cdot(\sqrt[4]{9})^2}=-4\cdot4\cdot\sqrt[4]{81}=\\\\=-16\cdot\sqrt[4]{3^4}=-16\cdot3=-48[/tex]
Wszystkie wykorzystane podczas obliczeń wzory
[tex](a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\a^m:a^n=a^{m-n}[/tex]
Pozdrawiam! ~ JulkaOdMatmy
