Question

If x=9+2 (10)^1/2 then find (x)^1/2+1/(x)^1/2​

Answer 1

Answer:

Step-by-step explanation:

$x=9+2\sqrt{10}\\ \\then\\\\\sqrt{x} +\dfrac{1}{\sqrt{x} }\\\\(\sqrt{x} +\dfrac{1}{\sqrt{x} })^2\\\\x+\dfrac{1}{x}+2*\sqrt{x}   *\dfrac{1}{\sqrt{x} }\\\\x+\dfrac{1}{x} +2$

put the value of x

$9+2\sqrt{10}  +\dfrac{1}{9+2\sqrt{10}} +2\\\\(9+2\sqrt{10})*(9+2\sqrt{10})+(9+2\sqrt{10})*\dfrac{1}{9+2\sqrt{10}} +2*(9+2\sqrt{10})\\\\81+40+36\sqrt{10} +1+18+4\sqrt{10}\\ \\140+40\sqrt{10}$