Помогите решить!( x^{2} +2)(2 x^{2} -9x+4)+9 x^{2} =0.. Created by danilaborziy. matematika-ru

Помогите решить!( x^{2} +2)(2 x^{2} -9x+4)+9 x^{2} =0...

danilaborziy @danilaborziy

July 2022 1 3 Report

Помогите решить!

( x^{2} +2)(2 x^{2} -9x+4)+9 x^{2} =0.

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NNNLLL54

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$(x^2+2)(2x^2-9x+4)+9x^2=0\\\\2x^4-9x^3+4x^2+4x^2-18x+8+9x^2=0\\\\2x^4-9x^3+17x^2-18x+8=0\\\\Podbiraem\; koren.\\\\x=1:\; 2-9+17-18+8=0\; \to \; x=1\; -\; koren\\\\(2x^4-9x^3+17x^2-18x+8):(x-1)=2x^3-7x^2+10x-8\\\\2x^4-9x^3+17x^2-18x+8=(x-1)(2x^3-7x^2+10x-8)\\\\2x^3-7x^2+10x-8=0\\\\Podbiraem\; koren.\\\\x=2:\; \; 2\cdot 8-7\cdot 4+10\cdot 2-8=0\; \to \; x=2\; -\; koren\\\\(2x^3-7x^2+10x-8):(x-2)=2x^2-3x+4\\\\2x^3-7x^2+10x-8=(x-2)(2x^2-3x+4)\\\\2x^2-3x+4=0\; ,\; \; D=-23$

2x⁴-9x³+17x²-18x+8 | x-1 2x³-7x²+10x-8 | x-2

-(2x⁴-2x³) |------------- -(2x³-4x²) |--------------

-------------------- 2x³-7x²+10x-8 ---------------- 2x²-3x+4

-7x³+17x²-18x+8 -3x²+10x-8

-(7x³+7x²) -(-3x²+6x)

------------------------ -------------------

10x²-18x+8 4x-8

-(10x²-10x) -(4x-8)

----------------- -----------------

-8x+8 0

-(-8x+8)

-------------

1 votes Thanks 1

danilaborziy Спасибо!!!

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