Question

solve for x
$= \sqrt{3{ \:} } x {}^{2} - \sqrt[2]{2}x - \sqrt[2]{3} = 0$
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Answer 1

Answer:

two values of x are

(1 + $\sqrt{7}$ )/( $\sqrt{2}.\sqrt{3}$ ) = 1.48

(1 - $\sqrt{7}$ )/( $\sqrt{2}.\sqrt{3}$ ) = -0.67

Step-by-step explanation:

$\sqrt[2]{x}$ means $\sqrt{x}$

$\sqrt{3}$ $x^{2}$ - $\sqrt{2}$$x^{}$ - $\sqrt{3}$ = 0

By sridharacharaya formula:

a = $\sqrt{3}$

b = -$\sqrt{2}$

c = -$\sqrt{3}$

$x^{}$ = ( $\sqrt{2}$ ± $\sqrt{2 + (4\sqrt{3}.\sqrt{3})  }$ )/( 2.$\sqrt{3}$ )

 = ( $\sqrt{2}$ ± $\sqrt{14}$ )/ ( 2.$\sqrt{3}$ )

when the sign is positive:

= ( $\sqrt{2}$ + $\sqrt{14}$ )/ ( 2.$\sqrt{3}$ )

= ( $\sqrt{2}$ ( 1 + $\sqrt{7}$) ) )/( $\sqrt{2}$.$\sqrt{2} .\sqrt{3}$ )

= (1 + $\sqrt{7}$ )/( $\sqrt{2}.\sqrt{3}$ )

= 1.48

when the sign is negative:

= ( $\sqrt{2}$ - $\sqrt{14}$ )/ ( 2.$\sqrt{3}$ )

= ( $\sqrt{2}$ ( 1 - $\sqrt{7}$) ) )/( $\sqrt{2}$.$\sqrt{2} .\sqrt{3}$ )

= (1 - $\sqrt{7}$ )/( $\sqrt{2}.\sqrt{3}$ )

= -0.67

two values of x are 1.48 and -0.67