Question

Solve the equation. 7x = 3x2 - 1 a. 7+ V61 Or 6 7 √61 c. -7+ V6 X= 7- 761 X= 6 or 12 12 b. -7+ √61 7- √61 d. X= 7+ √61 7-V61 or 6 = 6 12 12

Answer 1

reordering

`\begin{gathered} 7x=3x^2-1 \\ 7x-7x=3x^2-1-7x \\ 3x^2-7x-1=0 \end{gathered}`

then solve

`\begin{gathered} x_(1,\: 2)=(-\left(-7\right)\pm√(\left(-7\right)^2-4\cdot\:3\left(-1\right)))/(2\cdot\:3) \\ x_(1,\: 2)=(-\left(-7\right)\pm√(61))/(2\cdot\:3) \\ x_1=(-\left(-7\right)+√(61))/(2\cdot\:3),\: x_2=(-\left(-7\right)-√(61))/(2\cdot\:3) \\ for\text{ one} \\ x=\frac{-(-7)+\sqrt[]{61}}{2\cdot\: 3}=\frac{7+\sqrt[]{61}}{6} \\ or \\ x=\frac{-(-7)-\sqrt[]{61}}{2\cdot\: 3}=\frac{7-\sqrt[]{61}}{6} \end{gathered}`

answer:

`\begin{gathered} x=(7+√(61))/(6) \\ or \\ x=(7-√(61))/(6) \end{gathered}`