Докажите тождество (x-2y)(x+2y)x²+4y²)=x⁴-16y⁴

Question

Алгебра: Докажите тождество (x-2y)(x+2y)x²+4y²)=x⁴-16y⁴

Lerawsfghdsx · Accepted Answer

1) 2/(x+2) +5x/4(x+2) =13/8 -1/2 ; (8+5x)/4(x+2) =9/8  ||*8(x+2) 2(8+5x) =9(x+2); 16+10x =9x +18 ; 10x -9x =18 -16; x =2. (x+36)/(x³ -1) -(x+6)/(x-1) +(x²-x+16)/(x²+x+1) =0  || (x³ -1) * * *  ОДЗ:  x ≠1 * * * x+36 -(x+6)(x²+x+1) +(x-1)(x²-x+16) =0 ; x+36 -x³ -x² -x -6x² -6x -6 +x³-x² +16x -x²+x -16 =0; -9x² +11x +14 =0 ; 9x² -11x -14 =0 ; D =11² -4*9(-14) =121+504 =625=25²⇒√D =25; x₁ =(11-25)/(2*9) = -7/9 ; x₂ =(11+25)/(2*9) =36/18 =2. ответ : { -7/9 ; 2 }. 4x²/(x² -1)+(x-2)/(x+1) -(x+2)/(x-1) =0...

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