Chala kvadrat tenglamalar yuqori tartibli tenglamalar uch hadli tenglamalar

4-misol. x⁶-3x³-2=0 tenglama yechilsin.


Yechish: y=x³ deb belgilab y²-3y+2=0 yordamchi tenglama topa-miz, uning ildizlari y₁=1, y₂=2.
Natijada x³=1 va x³=2 tenglamalarga ega bo`lamiz. Bular (x- -1)(x²+x+1)=0 va tenglamalarga teng kuchlidir. Birinchisidan, x₁=1, ni, ikkinchisidan ni hosil qilamiz.


5-misol. 3x⁴+26x²-9 bikvadrat uchhad ko`paytuvchilarga ajratilsin.
Yechish: 3x<sup>4</sup>+26x<sup>2</sup>-9=0 tenglamani yechamiz: va dan x<sup>2</sup>=-9 dan x<sub>3</sub>=3i, x<sub>4</sub>=-3i ni topamiz va ni hosil qilamiz, yoki hosil bo`ladi (kompleks sonlar to`plamida), Haqiqiy sonlar to`plamida esa bo`ladi


Mashqlar

12 Quyidagi ikki hadli tenglamalarni yeching.

1) x³-8=0 5) x⁴-16=0
2) x³+8=0 6) x⁴+16=0
3) x⁵-32=0 7) x⁴-81=0
4) x⁵+32=0 8) x⁴+81=0

126. Quyidagi uch hadli tenglamalarni yeching:

1) x⁴+5x²-36=0 5) x⁴+3x²-18=0
2) x⁴-8x²-9=0 6) x⁴+4x²-32=0
3) x⁴-x²-6=0 7) x⁴+x²-1=0
4) x⁴+2x²-15=0 8) x⁴-2x²+4=0.

127. 1) Ildizlari 1-2i, 2-i bo`lgan haqiqiy koeffitsiyenti to`rtinchi darajali tenglamani tuzing.

2) Ildizlari 1, 1-2i, 2-i bo`lgan haqiqiy koeffitsiyenti beshinchi darajali tenglamani tuzing.
Javoblar: 12 2) x₁=-2, 4)
k=0,1,2,3,4; 6) 8) .

126. 2) 3; i; 4) 6)

127. 2) x⁵-7x⁴+24x³-48x²+55x-25=0.