Question

zad 1

a) (x-2y)²- (x+1)²

b) 3(x-5)²- (2x-1)²

c) (x-3)²- 2(x-1)²

d) (x+√2)²+ 2(x-√2)²

zad 2

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Answer 1

zad1

a) (x-2y)²- (x+1)²=x²-4xy+4y²-(x²+2x+1)=x²-4xy+4y²-x²-2x-1=-4xy-2x+4y²

b) 3(x-5)²- (2x-1)²=3(x²-10x+25)-(4x²-4x+1)=3x²-30x+75-4x²+4x-1=-x²-26x+74

c) (x-3)²- 2(x-1)²=(x²-6x+9)-2(x²-2x+1)=x²-6x+9-2x²+4x-2=-x²-2x+7

d)  (x+√2)²+ 2(x-√2)²=(x²+2√2x+√4)+2(x²-2√2x+√4)=x²+2√2x+2+2x²-4√2x+4=3x²-2√2x+6

zad2

a) P₁=(a-r)²π=a²-2ar+r²π     P₂=πr²                         P=πr²

P=P₁+P₂=a²-2ar+r²π+r²π=a²-2ar+2r²π

P=a²-2ar+2r²π=a²-2r(a-rπ)

 

b)½(x+1)=r      P₁=(½x+½)²π=¼x²+½x+¼π      P₂=(½x)²π=¼x²π

P=P₁-P₂=¼x²+½x+¼π-¼x²π=½x+¼π=½(x+½π)

P=½(x+½π)