Math, asked by reshmivishanth, 10 months ago

solve the following quadratic equations by formula method
 \sqrt{2 {x}^{2} }  - 6x \times 3 \sqrt{2 = 0

Answers

Answered by amitkumar44481
2

Correct Question :

Q. Solve the following quadratic equation by formula method

\tt \sqrt{2} {x}^{2} - 6x + 3 \sqrt{2} = 0.

AnsWer :

x = 3 + √3/√2 and x = 3 - √3 /√2.

Solution :

We have,

Quadratic Equation,

 \tt \dagger \:  \:  \:  \:  \:  \sqrt{2}  {x}^{2}   - 6x + 3 \sqrt{2}  = 0.

We have, two method to Find its zeros.

  • Splitting the Middle term.
  • Quadratic Formula.

Compare with General Equation.

 \tt \dagger \:  \:  \:  \:  \:  a {x}^{2}  + bx + c = 0. \:  \:  \:  \:  \:  \red{a \neq0}.

Let try To solve by Quadratic Formula.

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

Where as,

  • a = √2.
  • b = -6.
  • c = 3√2.

 \tt\mapsto x =  \dfrac{6 \pm \sqrt{ { (- 6)}^{2} - 4  \times \sqrt{2} \times 3 \sqrt{2}   } }{2 \sqrt{2} }

 \tt\mapsto x =  \dfrac{6 \pm  \sqrt{36 - 24} }{2 \sqrt{2} }

 \tt\mapsto x =  \dfrac{6 \pm \sqrt{12} }{2 \sqrt{2} }

 \tt\mapsto x =  \dfrac{6 \pm2 \sqrt{3} }{2 \sqrt{2} }

 \tt\mapsto x =  \dfrac{2(3 \pm \sqrt{3}) }{2 \sqrt{2} }

 \tt\mapsto x =  \dfrac{3 \pm \sqrt{3} }{ \sqrt{2} }

Either,

 \tt x =  \dfrac{3  +  \sqrt{3} }{ \sqrt{2} } \:  \:  \:   \red{ or} \:  \:  \:   x =  \dfrac{3   -   \sqrt{3} }{ \sqrt{2} }

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