Question

if x=3+2√2, find the value of (√x-1/√x)​

Answer 1

Answer:

2-√2

Step-by-step explanation:

$x=3+2\sqrt2\\x=2+1+2\sqrt2\\x=\sqrt2^2+1^2+2(1)(\sqrt2)\\x=(\sqrt2+1)^2\\\sqrt x=\sqrt2+1\\\\\frac{\sqrt2+1-1}{\sqrt2+1}\\\\=\frac{\sqrt2}{\sqrt2+1}\\\\=\frac{\sqrt2}{\sqrt2+1}*\frac{\sqrt2-1}{\sqrt2-1}\\\\=\frac{\sqrt2^2-\sqrt2}{\sqrt2^2-1^2}\\\\=\frac{2-\sqrt2}{2-1}=2-\sqrt2$

Hope it helps!

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