Предмет: Алгебра, автор: Katуa

Ребят, пожалуйста помогите решить:

 

 системы уравнений:

у-5х=1

у^2-13х=23

 

 

х-4у=3

х^2-21у=28

Упростить:


sqrt(4x)+sqrt(64x)-sqrt(81x)

sqrt(49x)-sqrt(16x)+sqrt(25x)

 

Ответы

Автор ответа: asya0401
0

1)

у-5х=1

у^2-13х=23

Выразим из первого уравнения y:

у=1+5х

Подставим (1+5х) вместо y во второе уравнение:

(1+5х)^2-13x=23

1+10x+25x^2-13x-23=0

25x^2-3x-22=0

Найдём дискириминант: D=b^2-4ac=3^2+3*25*22=2209=47^2

x1=3+47/50=50/50=1

x2=3-47/50=-44/50 (сократим дробь на 2) =-22/25

если х=1,то у=1+5х=1+5*1=1+5=6

если х=-22/25 , то у=1+5х=1- 5*22/25=1-4 2/5 (одна целая минус 4 целых две пятых)=5/5-4 2/5=-3 2/5 (минус 3 целых две пятых)

Ответ: (1;6), (-22/25; -3 2/5)

 2)

х-4у=3

х^2-21у=28

Выразим из первого уравнения х:

х=3+4y

Подставим (3+4y) вместо х во второе уравнение:

(3+4y)^2-21у=28

9+24у+16у^2-21у-28=0

16^y+3у-19=0

Найдём дискириминант:D=b^2-4ac=3^2+ 4*16*19=9+1216=1225=35^2

y1=-3+35/32=32/32=1

y2=-3-35/32=-38/32=-1 3/16 (минус 1 целая три шестнадцатых)   

если y=1,то x=3+4y=3+4*1=3+4=7

если y=-1 3/16  , то x=3+4y=3- 4*1 3/16= -1 3/4  (минус 1 целая три четвёртых)

Ответ: (7:1), (-1 3/4; -1 3/16)


Упростить:

1.

sqrt(4x)+sqrt(64x)-sqrt(81x)

вытаскиваем корни из 4,64,81

 

2.

sqrt(49x)-sqrt(16x)+sqrt(25x)

вытаскиваем корни из 49,16,25


 

 

 

 

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