Question

True or False: 3 is a solution to the equation-2? + 2x + 4 = 1TrueFalse

Answer 1

We have the equation:

`\begin{gathered} -x^2+2x+4=1 \\ -x^2+2x+4-1=0 \\ -x^2+2x+3=0 \end{gathered}`

This is a quadratic equation, so we can solve it like this:

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ a=-1,b=2,c=3 \\ \\ x_(1,2)=(-2\pm√(2^2-4\cdot(-1)\cdot3))/(2\cdot(-1))=(-2\pm√(4+12))/(-2)=(-2\pm√(16))/(-2)=(-2\pm4)/(-2) \\ \\ x_1=(-2+4)/(-2)=(2)/(-2)=-1 \\ \\ x_2=(-2-4)/(-2)=(-6)/(-2)=3 \end{gathered}`

The solutions to this equation are x=-1 and x=3.

So it is TRUE that 3 is a solution to the equation.