Question

x^2+x+1/√2=0 Solve the following equation​

Answer 1

Solution :

We have, Equation.

$\tt \dagger \: \: \: \: \: {x}^{2} + x + \dfrac{1}{ \sqrt{2} } = 0.$

Compare with General Formula.

$\tt \dagger \: \: \: \: \: a {x}^{2} + bx + c = 0.$

$\tt \dagger \: \: \: \: \: \red {a \neq 0.}$

A/Q,

$\tt : \implies {x}^{2} + x + \dfrac{1}{ \sqrt{2} } = 0.$

$\tt : \implies \dfrac{ \sqrt{2 } {x}^{2} + \sqrt{2}x + 1 }{ \sqrt{2} } = 0.$

$\tt : \implies \sqrt{2} {x}^{2} + \sqrt{2} x + 1 = 0.$

Where as,

• a = √2.
• b = √2.
• c = 1.

$\tt \dagger \: \: \: \: \: x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

$\tt : \implies \dfrac{ - \sqrt{2} \pm \sqrt{ { (\sqrt{2}) }^{2} - 4 \times \sqrt{2} \times 1} }{2 \sqrt{2} }$

$\tt : \implies \dfrac{ - \sqrt{2} \pm \sqrt{ { 2} - 4 \sqrt{2} } }{2 \sqrt{2} }$