Question

Help plsss

1/2x^2 =2
If x1 and x2 are the solutions to the equation above,
what is the value of x1 + x2?
A) 0
B) 1
C) 2
D) 4

Answer 1

⭐ Development:

• Having the expression, let's modify it so it becomes a 2nd degree equation:

`\large {\text {$ \sf \cfrac{1}{2x^2} -2 = 0 $}}`

• Now, we will multiply per 2x² both sides of equation...

`\large {\text {$ \sf \cfrac{1}{2x^2}\cdot \:2x^2-2\cdot \:2x^2=0\cdot \:2x^2 $}`

`\searrow`

`\large {\text {$ \sf 1-4x^2=0$}}`

• We have to write in standard form...

`\large {\text {$ \sf -4x^2+1 = 0 $}}`

`\large {\text{$\sf x=\cfrac{-b\pm√(b^2-4ac)}{2a} \quad\rightarrow\quad x=\cfrac{-0\pm√(0^2-4\cdot (-4) \cdot1) }{2\cdot (-4) } \:\rightarrow\:\: x=\cfrac{-0^2 \pm4}{2 \cdot(-4)} $}}`

`\huge {\text {$ \sf \downarrow$}}`

`\large {\text {$\sf {\bf x_1} = \cfrac{-0+4}{2\left(-4\right)}= \cfrac{-1}{2} $}}`
`\large {\text {$\sf {\bf x_2 }=\cfrac{-0-4}{2\left(-4\right)} = \cfrac{1}{2} $}}`

• At this point, we're going to add the values ​​of x₁ and x₂:

`\large {\boxed {\boxed { \bf x_1 + x_2= -\cfrac{1}{2}+ \cfrac{1}{2} = 0} }}`

`\huge {\text {$ \it Alternative \: A $}}`