PILNE NA JUTRO-DAM NAJLEPSZĄ!!! Rozwiąż zadania podane w załączniku.

zad. 1 a) (2y-3)^2 -(3y-2)(3y+2)= (4y^2-6y-6y+9)-(9y^2+6y-6y-4)=4y^2-12y+9-9y^2+4= -5y^2-12y+13 b)(5y+1)(1-5y)-(1+5y)^2= (5y-25y^2+1-5y)-(1+5y+5y+25y^2)=-25y^2+1-1-5y-5y-25y^2=-50y^2+10y zad2 a) (2x-1)^2-(2x-1)(1+2x)-(2x+1)^2=(2√2 -1)^2-(2√2-1)(1+2√2)-(2√2+1)^2=(4-1)-(2√2-1)(1+2√2)-(4+1)=3-(2√2+8-1-2√2)-5=3-2√2-8+1+2√2-5=-9  

zad 1 a)(2y-3)²-(3y-2)(3y+2)=4y²-12y+9-9y²+4=-5y²-12y+13 b)(5y+1)(1-5y)-(1+5y)²=1-25y²-1-10y-25y²=-50y²-10y c)(x²-3)²+(3+x²)²-(x²-1)²=x⁴-6x²+9+9+6x²+x⁴-x⁴+2x-1=x⁴+2x+17 d)(x²-2)(x²+2)-(4-x²)(x²+4)=x⁴-4-16+x⁴=2x⁴-20 zad 2 a)(2x-1)²-(2x-1)(1+2x)-(2x+1)²=4x²-4x+1-4x²+1-4x²-4x-1=-4x²-8x+1= =-4(√2)²-8*√2+1=-8-8√2+1=-7-8√2 b)(√5+x)²-(√5-x)²+(x+√5)(√5-x)=5+2√5x+x²-5+5=2√5x-x²+5-x²=-x²+4√5+5= =-(√5-1)²+4√5(√5-1)+5=-5+2√5+1+20+4√5+5=21+6√5 zad 3 a)(x-y)(x+y)+(x+2y)(x-2y)=x²-y²+x²-4y²=2x²-5y²=2(√2)²-5(1-√3)²=4-5+10√3-15=-16+10√3 b)(3x+y)(3x-y)-(x-5y)(x+5y)=9x²-y²-x²+25y²=8x²+24y²=8(1+√3/2)²+24(1+√2)²= 8(1+√3+3/4)+24(1+2√2+2)=8+8√3+6+24+48√2+48=86+8√3+48√2 c) (y-3x)²-(y-4x)²-6xy=y²-6xy+9x²-y²+8xy-16x²-6xy=-7x²-4xy= = -7(1/(√2-1))²-4*1/(√2-1)*√2=-7-4√2/(√2-1)=-(7(√2-1)/(√2-1)-4√2/(√2-1)= (-11√2+7)/(√2-1) d)1/(2x²-6)=1/(2(1+√2)²-6)=1/(2(1+2√2+2)-6)=1/4√6 e)(x+1)/(x²-4)=(-1+√3+1)/((-1+√3)²-4)=√3/(1-2√3+3-4)=-√3/2√3=-1/2