Ответ:
Объяснение:
a)x²+2x-63=0
x₁+x₂=-2 x₁x₂=-63 x₁=-9 x₂=7
x²+2x-63=(x+9)(x-7)
49-x²=7²-x²=(7-x)(7+x)
(x+9)(x-7)/(7-x)(7+x)=-(x+9)(7-x)(7-x)(7+x)=(x+9)/(7+x)
б)6x²+x=x(6x+1)
6x²-17x-3=0
D=289-4·6·(-3)=361
x₁=(17-19)/12=-1/6 x₂=(17+19)/12=3
6x²-17x-3=6(x+1/6)(x-3)=(6x+1)(x-3)
(6x+1)(x-3)/x(6x+1)=(x-3)/x
в)8x-x²=x(8-x)
x²-3x-40=0
x₁+x₂=3 x₁x₂=-40 x₁=8 x₂=-5
x²-3x-40=(x+5)(x-8)
x(8-x)/(x+5)(x-8)=-x(x-8)/(x+5)(x-8)=-x/(x+5)
г)5x²-12x+4=0
D=144-4·5·4=64
x₁=(12-8)/10=2/5 x₂=(12+8)/10=2
5x²-12x+4=5(x-2/5)(x-2)=(5x-2)(x-2)
25x²-4=(5x)²-2²=(5x-2)(5x+2)
(5x-2)(x-2)/(5x-2)(5x+2)=(x-2)/(5x+2)
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Answers & Comments
Ответ:
Объяснение:
a)x²+2x-63=0
x₁+x₂=-2 x₁x₂=-63 x₁=-9 x₂=7
x²+2x-63=(x+9)(x-7)
49-x²=7²-x²=(7-x)(7+x)
(x+9)(x-7)/(7-x)(7+x)=-(x+9)(7-x)(7-x)(7+x)=(x+9)/(7+x)
б)6x²+x=x(6x+1)
6x²-17x-3=0
D=289-4·6·(-3)=361
x₁=(17-19)/12=-1/6 x₂=(17+19)/12=3
6x²-17x-3=6(x+1/6)(x-3)=(6x+1)(x-3)
(6x+1)(x-3)/x(6x+1)=(x-3)/x
в)8x-x²=x(8-x)
x²-3x-40=0
x₁+x₂=3 x₁x₂=-40 x₁=8 x₂=-5
x²-3x-40=(x+5)(x-8)
x(8-x)/(x+5)(x-8)=-x(x-8)/(x+5)(x-8)=-x/(x+5)
г)5x²-12x+4=0
D=144-4·5·4=64
x₁=(12-8)/10=2/5 x₂=(12+8)/10=2
5x²-12x+4=5(x-2/5)(x-2)=(5x-2)(x-2)
25x²-4=(5x)²-2²=(5x-2)(5x+2)
(5x-2)(x-2)/(5x-2)(5x+2)=(x-2)/(5x+2)