Question

If x = 6- root 35 then find the value of x + 1/x

Answer 1

Step-by-step explanation:

Substituting value of x in x +1/x, we get,

$6 + \sqrt{35} + \frac{1}{6 + \sqrt{35} }$

Taking LCM,

$\frac{(6 + \sqrt{35})(6 + \sqrt{35}) + 1 }{6 + \sqrt{35} }$

$\frac{ {(6 + \sqrt{35} ) }^{2} + 1 }{6 + \sqrt{35} }$

Expanding the equation by using idendity,

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

$\frac{36 + 12 \sqrt{35} + 35 + 1 }{6 + \sqrt{35} }$

$\frac{72 + 12 \sqrt{35} }{6 + \sqrt{35} }$

Rationalising the denominator,

$\frac{72 + 12 \sqrt{35} }{6 + \sqrt{35} } \times \frac{6 - \sqrt{35} }{6 - \sqrt{35} }$

$\frac{(72 + 12 \sqrt{35} )(6 - \sqrt{35}) }{36 - 35}$

$572 - 72 \sqrt{35} + 72 \sqrt{35} - 420$

$= 152$

Mark as Brainliest....