Question

Из многочленов А=3х^2+7х-1 и В=-3х^2-5х+1 составлено выражение Р=А^3+3А^3В+3АВ^2+В^3. Найдите значение Р(х) при х=0,2

Answer 1

$P=A^3+3A^3B+3AB^2+B^3=(A+B)^3=\\\\ =([3x^2+7x-1]+[-3x^2-5x+1])^3=\\\\ =(3x^2+7x-1-3x^2-5x+1)^3=(2x)^3=\\\\ =(2*0.2)^3=(0.4)^3=(\frac{4}{10})^3=\frac{4^3}{10^3}=\frac{64}{1000}=0.064$

Answer 2

To find the value of the expression P(x) = A^3 + 3A^3B + 3AB^2 + B^3 when x = 0.2, we first need to calculate the values of A and B at x = 0.2.

For A: A = 3x^2 + 7x - 1 A(0.2) = 3(0.2)^2 + 7(0.2) - 1 A(0.2) = 3(0.04) + 1.4 - 1 A(0.2) = 0.12 + 1.4 - 1 A(0.2) = 1.52 - 1 A(0.2) = 0.52

For B: B = -3x^2 - 5x + 1 B(0.2) = -3(0.2)^2 - 5(0.2) + 1 B(0.2) = -3(0.04) - 1 + 1 B(0.2) = -0.12

Now, we can substitute the values of A and B into the expression P(x):

P(x) = A^3 + 3A^3B + 3AB^2 + B^3 P(0.2) = (0.52)^3 + 3(0.52)^3(-0.12) + 3(0.52)(-0.12)^2 + (-0.12)^3 P(0.2) = 0.140608 + 3(0.140608)(-0.12) + 3(0.52)(0.0144) + (-0.001728) P(0.2) = 0.140608 - 0.05059136 + 0.0221184 - 0.001728 P(0.2) = 0.11020604

Therefore, the value of P(x) when x = 0.2 is approximately 0.1102.