Question

the length of two sides of a triangle are, side 1 , 8x^2-5x-2, side 2 ,7x-x^2+3
the perimeter of the triangle is 4x^3-3x^2+2x-6
what is the length of the third side of the triangle?

Answer 1

Let \(y\) be the length of the third side.

The perimeter is the sum of the three side lengths:
\[\begin{align*}P&=\color{red}{s_1}+\color{blue}{s_2}+\color{green}{s_3}\\
4x^3-3x^2+2x-6&=\color{red}{(8x^2-5x-2)}+\color{blue}{(7x-x^2+3)}+\color{green}{y}\end{align*}\]
Solve for \(y\).

Answer 2

how would i do that, sorry

Answer 3

\[\begin{align*}
4x^3-3x^2+2x-6-\color{red}{(8x^2-5x-2)}-\color{blue}{(7x-x^2+3)}&=\color{green}{y}\\
4x^3-3x^2+2x-6-8x^2+5x+2-7x+x^2-3&=\color{green}{y}\\
4x^3-10x^2+0x-7&=\color{green}{y}\\
y&=4x^3-10x^2-7
\end{align*}\]