Find the root of \sqrt{2x { }^(2) } + x + √(2) = 0 ​

Question

Find the root of

`\sqrt{2x { }^(2) } + x + √(2) = 0`
​

Answer 1

The root of x = -2 + √2

Explanation:

Step(i):-

Given
`\sqrt{2x^(2) } + x +√(2) = 0`

⇒
`√(2) } ( x^2 ) ^{(1)/(2) } + x +√(2) = 0`

⇒
`√(2)x + x +√(2) = 0`

⇒
`(√(2) + 1) x = - √(2)`

`x = (-√(2) )/((√(2) + 1))`

Step(ii):-

Rationalizing

`x = (-√(2) )/((√(2) + 1)) X ((√(2) - 1))/((√(2) - 1))`

Apply ( a-b ) ( a+b) = a²-b²

`x = (-√(2)(√(2) -1) )/((√(2))^(2) - 1^(2) )) = (-(2-√(2) )/(2-1)`

The root of x = -2 + √2