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Question Number 177856 by mathlove last updated on 10/Oct/22

$$p\left(x\right)+p(x-1)=2x+4$$$$p\left(x\right)=?$$

Answered by blackmamba last updated on 10/Oct/22

$$p\left(x\right)=ax+b$$$$p(x-1)=a(x-1)+b=ax+b-a$$$$\Rightarrow p\left(x\right)+p(x-1)=2ax+2b-a=2x+4$$$$\{\begin{array}{l}2a=2\Rightarrow a=1\\ 2b-2=4\Rightarrow b=3\end{array}$$$$\therefore p\left(x\right)=2x+3$$

Commented by mathlove last updated on 10/Oct/22

$$thanks$$

Commented by Tinku Tara last updated on 10/Oct/22

$$\mathrm{Small}\mathrm{caculation}\mathrm{error}.\mathrm{pls}\mathrm{check}$$$$a=1$$$$2b-a=4\Rightarrow b=2.5$$$$p\left(x\right)=2x+2.5$$

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