Question

Сократите дробь. Алгебра 10 класс.

Answer 1

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)