Question

if x =√7+3, find the value of√x+1/√x​

Answer 1

Answer:

4

Step-by-step explanation:

$x = 7 + 4 \sqrt{3} \\ \\ x = 4 + 3 + 4 \sqrt{3} \\ \\ x = (2) {}^{2} + ( \sqrt{3} ) {}^{2} + 2 \times 2 \times \sqrt{3} \\ \\ x = (2 + \sqrt{3} ) {}^{2} \\ \\ \bf \sqrt{x} = 2 + \sqrt{3}$

Now,

$\frac{1}{ \sqrt{x} } = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \frac{1}{ \sqrt{x} } = \frac{2 - \sqrt{3} }{2 {}^{2} - \sqrt{3} {}^{2} } \\ \\ \frac{1}{ \sqrt{x} } = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \bf \frac{1}{ \sqrt{x} } = 2 - \sqrt{3}$

Therefore,

$\sqrt{x} + \frac{1}{ \sqrt{x} } = 2 + \sqrt{3} + 2 - \sqrt{3} \\ \\ \sqrt{x} + \frac{1}{ \sqrt{x} } = 2 + 2 \\ \\ \boxed{ \bf \sqrt{x} + \frac{1}{ \sqrt{x} } = 4}$