Zad,1 [latex](4-2x)^2=16-16x+4x^2\[/latex] Odp:D Zad,2 [latex]9a^2-6a+1=(-3a)^2+2*(-3a)+1^2=(1-3a)^2[/latex] Odp:D Zad,3 korzystam z wzoru (a-b)(a+b)=a²-b² [latex](2x-1)^2-1=(2x-1-1)(2x-1+1)=(2x-2)*2x=4x^2-4x[/latex] Odp: C Zad,4 [latex]a)\(5+sqrt3x)^2=5^2+2*5*sqrt3x+(sqrt3x)^2=25+10sqrt3x+3x^2\b)\(frac{1}{6}x-2)^2=frac{1}{36}x^2-frac{2}{3}x+4\c)\(0,2x+sqrt7)(0,2x-sqrt7)=(0,2x)^2-(sqrt7)^2=0,04x^2-7[/latex] Zad,5 [latex](3a-2)^2-2(a+2)(a-2)=9a^2-12a+4-2(a^2-4)=\=9a^2-12a+4-2a^2+8=7a^2-12a+12\a=-sqrt3\7*(-sqrt3)^2-12*(-sqrt3)+12=21+12sqrt3[/latex] Zad,6 [latex](1+2sqrt3)^2-(sqrt3-2)^2+(1-sqrt7)(1+sqrt7)=\=1+4sqrt3+12-(3-4sqrt3+4)+1-7=\=4sqrt3-3+4sqrt3-4+7=8sqrt3[/latex] Zad,7 [latex](1+3sqrt2)^2=1+6sqrt2+18=19+6sqrt2approx19+8,46approx27,46\sqrt{29}^2=29\29>27,46\sqrt{29}>1+3sqrt2[/latex] Zad,8 [latex]a)\(x-4)(x+4)-(2x+1)^2+(x-5)^2=\=x^2-16-(4x^2+4x+1)+x^2-10x+25=\x^2-16-4x^2-4x-1+x^2-10x+25=\=-2x^2-14x+8\b)\-(-5x-2)^2-(-6x-3)^2=\=-(25x^2+20x+4-(36x^2+36x+9)=\=-25x^2-20x-4-36x^2-36x-9=\=-61x^2-56x-13[/latex] Zad,9 [latex](sqrt{3-2sqrt2}-(sqrt{3+2sqrt2})^2=\=(sqrt{3-2sqrt2})^2-2(sqrt{3-2sqrt2})(sqrt{3+2sqrt2})+(sqrt{3+2sqrt2})^2=\=3-2sqrt2-2(9-4*2)+3+2sqrt2=9-2=7[/latex] Zad,10 [latex]x^4-[(x-1)^2+(x-1)(x+1)]^2=\x^4-[(x-1)(x-1+x+1)]^2=\=x^4-[(x-1)*2x]^2=\x^4-(2x^2-2x)^2=\=x^4-(4x^4-8x^3+4x^2)=\=x^4-4x^4+8x^3-4x^2=\=-3x^4+8x^3-4x^2[/latex] Zad,11 [latex](a^2+b^2)^2=a^4+2a^2b^2+b^4\a^2+b^2=sqrt{a^4+2a^2b^2+b^4}=sqrt{28+2*2^2}=\=sqrt{28+8}=sqrt{36}=6[/latex] Zad,12 [latex]x+ frac{1}{x}=3|^2\(x+ frac{1}{x})^2=3^2\x^2+2x*frac{1}{x}+frac{1}{x^2}=9\ x^2+2+frac{1}{x^2}=9\x^2+frac{1}{x^2}=9-2\{x^2}=9\x^2+frac{1}{x^2}=7[/latex]
