Question

Решите уравнения (33.15-33.16):
1) (x + 2)³ - (х – 2)³ -=2x (6х + 2);
2) (х+3)³- (х - 4)³ = 21x² + 7;​

Answer 1

Объяснение:

$1)\ (x+2)^3-(x-2)^3=2x*(6x+2)\\(x+2-(x-2)*((x+2)^2+(x+2)*(x-2)+(x-2))=12x^2+4x\\(x+2-x+2)*(x^2+4x+4+x^2-4+x^2-4x+4)=12x^2+4x\\4*(3x^2+4)=12x^2+4x\\12x^2+16=12x^2+4x\\4x=16\ |:4\\x=4.$

Ответ: x=4.

$2)\ (x+3)^3-(x-4)^3=21x^2+7\\(x+3-(x-4))*((x+3)^2+(x+3)*(x-4)+(x-4)^2)=21x^2+7\\(x+3-x+4)*(x^2+6x+9+x^2-x-12+x^2-8x+16=21x^2+7\\7*(3x^2-3x+13)=21x^2+7\\21x^2-21x+91=21x^2+7\\21x=84\ |:21\\x=4.$

Ответ: x=4.