f ( x) = -6x ³ + 4x – 8x mũ 5 + 0,25 + 10x mũ 6
g ( x ) = 0,75 – 5x mũ 4 + 3x ² + 9x – 7x mũ 6
Tính :
A, f ( x ) + g (x)
B, g ( x) – f (x)
f ( x) = -6x ³ + 4x – 8x mũ 5 + 0,25 + 10x mũ 6
g ( x ) = 0,75 – 5x mũ 4 + 3x ² + 9x – 7x mũ 6
Tính :
A, f ( x ) + g (x)
B, g ( x) – f (x)
Đáp án:
A, 3$x^{6}$ – 8$x^{5}$ – 5$x^{4}$ – 6$x^{3}$ + 3$x^{2}$ + 13x + 1
B, 17$x^{6}$ – 8$x^{5}$ + 5$x^{4}$ – 6$x^{3}$ – 3$x^{2}$ – 5x – 0,5
Giải thích các bước giải:
Theo bài ra:
f(x) = -6$x^{3}$ + 4x – 8$x^{5}$ + 0,25 + 10$x^{6}$
g(x) = 0,75 – 5$x^{4}$ + 3$x^{2}$ + 9x – 7$x^{6}$
A, f(x) + g(x) = (-6$x^{3}$ + 4x – 8$x^{5}$ + 0,25 + 10$x^{6}$) + (0,75 – 5$x^{4}$ + 3$x^{2}$ + 9x – 7$x^{6}$)
= (10$x^{6}$ – 7$x^{6}$) – 8$x^{5}$ – 5$x^{4}$ – 6$x^{3}$ + 3$x^{2}$ + (4x + 9x) + (0,25+0,75)
= 3$x^{6}$ – 8$x^{5}$ – 5$x^{4}$ – 6$x^{3}$ + 3$x^{2}$ + 13x + 1
B, f(x) – g(x) = (-6$x^{3}$ + 4x – 8$x^{5}$ + 0,25 + 10$x^{6}$) – (0,75 – 5$x^{4}$ + 3$x^{2}$ + 9x – 7$x^{6}$)
= (10$x^{6}$ + 7$x^{6}$) – 8$x^{5}$ + 5$x^{4}$ – 6$x^{3}$ – 3$x^{2}$ + (4x – 9x) + (0,25-0,75)
= 17$x^{6}$ – 8$x^{5}$ + 5$x^{4}$ – 6$x^{3}$ – 3$x^{2}$ – 5x – 0,5