Question

7x=2x²+1, solve the equation ​

Answer 1

`x =(7+√(41))/(4),(7-√(41))/(4)`

Explanation:

The given equation is ,

`\longrightarrow 7x = 2x^2+1`

We can rewrite it as ,

`\longrightarrow 2x^2-7x + 1=0`

On comparing with the standard form of quadratic equation
`ax^2+bx + c` , we have ;

• 
  `a = 2`
• 
  `b = - 7`
• 
  `c = 1`

On using the quadratic formula , we have;

`\longrightarrow x = (-b \pm √(b^2-4ac))/(2a)\\`

`\longrightarrow x =(-(-7)\pm√((-7)^2-4(2)(1)))/(2(2)) \\`

`\longrightarrow x =(7\pm√(49-8))/(4)\\`

`\longrightarrow x =(7\pm√(41))/(4)`

separate the solutions ,

`\longrightarrow x =(7+√(41))/(4),(7-√(41))/(4)`

And we are done !