Question

Please answer as soon as possible
☺☺​

Answer 1

Answer:

p(2) - p(1) + $p(\dfrac{1}{2})$ = $\dfrac{33}{8}$

Step-by-step explanation:

Equation is-

p(x) = $x^{3}-4x+3$      ------------------------ 1

Find p(2) - p(1) + $p(\dfrac{1}{2})$

Put x = 2 in equation 1

p(2) = $2^{3} - 4(2) + 3$

      = 8 - 8 + 3

p(2) = 3

Put x = 1 in equation 1

p(1) = $1^{3} - 4(1) + 3$

     = 1 - 4 + 3

p(1) = 0

Put x = $\dfrac{1}{2}$ in equation 1

$P(\dfrac{1}{2}) = \dfrac{1^{3}}{2^{3}} -4 \times \dfrac{1}{2}+3 \\\\\\= \dfrac{1}{8} - 2+3$

                                $= \dfrac{1}{8}+ 1 \\\\ = \dfrac{1+8}{8} \\P(\dfrac{1}{2}) = \dfrac{9}{8}$

Now  p(2) - p(1) + $p(\dfrac{1}{2})$ = 3 + 0 + $\dfrac{9}{8}$

 = $\dfrac{3 \times 8+9}{8}$

 = $\dfrac{24+9}{8}$

p(2) - p(1) + $p(\dfrac{1}{2})$ = $\dfrac{33}{8}$

Answer 2

Answer:

p(2) - p(1) + p(\dfrac{1}{2})p(21) = \dfrac{33}{8}833

Step-by-step explanation:

Equation is-

p(x) = x^{3}-4x+3x3−4x+3      ------------------------ 1

Find p(2) - p(1) + p(\dfrac{1}{2})p(21)

Put x = 2 in equation 1

p(2) = 2^{3} - 4(2) + 323−4(2)+3

      = 8 - 8 + 3

p(2) = 3

Put x = 1 in equation 1

p(1) = 1^{3} - 4(1) + 313−4(1)+3

     = 1 - 4 + 3

p(1) = 0

Put x = \dfrac{1}{2}21 in equation 1

$$\begin{lgathered}P(\dfrac{1}{2}) = \dfrac{1^{3}}{2^{3}} -4 \times \dfrac{1}{2}+3 \\\\\\= \dfrac{1}{8} - 2+3\end{lgathered}$$

                                $$\begin{lgathered}= \dfrac{1}{8}+ 1 \\\\ = \dfrac{1+8}{8} \\P(\dfrac{1}{2}) = \dfrac{9}{8}\end{lgathered}$$

Now  p(2) - p(1) + $$p(\dfrac{1}{2})$$ = 3 + 0 + $$\dfrac{9}{8}$$

 = $$\dfrac{3 \times 8+9}{8}$$

 = $$\dfrac{24+9}{8}$$

p(2) - p(1) + $$p(\dfrac{1}{2})$$ = $$\dfrac{33}{8}$$