Question

if a=7-4√3 find the value of √a+1/√a
plz answer....this... : )

Answer 1

hii....here is your answer

Answer 2

$Given : 7 - 4 \sqrt{3}$

$\frac{1}{a} = \frac{1}{7 - 4 \sqrt{3} }$

On rationalizing we get

$\frac{1}{7 - 4 \sqrt{3} } * \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} }$

$\frac{7 + 4 \sqrt{3} }{7^2 - (4 \sqrt{3})^2 }$

$\frac{7 + 4 \sqrt{3} }{49 - 48}$

$\frac{7 + 4 \sqrt{3} }{1}$

$\frac{1}{a} = 7 + 4 \sqrt{3}$

Now,

$a + \frac{1}{a} = 7 - 4 \sqrt{3} + 7 + 4 \sqrt{3}$

$a + \frac{1}{a} = 14$

Now,

$( \sqrt{a} + \frac{1}{ \sqrt{a} })^2 = a + \frac{1}{a} + 2 \sqrt{a} * \frac{1}{ \sqrt{a} }$


$( \sqrt{a} + \frac{1}{ \sqrt{a} } )^2 = 14 + 2$

$( \sqrt{a} + \frac{1}{ \sqrt{a} } )^2 = 16$

$\sqrt{a} + \frac{1}{ \sqrt{a} } = 4.$



Hope this helps!