Question
If $\text{x}=\sqrt2-1,$ then write the value of $\frac{1}{\text{x}}.$
✓
Answer
Given that $\text{x}=\sqrt2-1.$ Hence $\frac{1}{\text{x}}$ is given as
$\frac{1}{\text{x}}=\frac{1}{\sqrt2-1}$
We know that rationalization factor for $\sqrt2-1$ is $\sqrt2+1.$ We will multiply each side of the given expression $\frac{1}{\sqrt2-1}$ by $\sqrt2+1,$ to get
$\frac{1}{\sqrt2-1}\times\frac{\sqrt2+1}{\sqrt2+1}=\frac{\sqrt2+1}{\big(\sqrt2\big)^2-(1)^2}$
$=\frac{\sqrt2+1}{\sqrt2-1}$
$=\sqrt2+1$
Hence the value of the given expresion is $\sqrt2+1.$
$\frac{1}{\text{x}}=\frac{1}{\sqrt2-1}$
We know that rationalization factor for $\sqrt2-1$ is $\sqrt2+1.$ We will multiply each side of the given expression $\frac{1}{\sqrt2-1}$ by $\sqrt2+1,$ to get
$\frac{1}{\sqrt2-1}\times\frac{\sqrt2+1}{\sqrt2+1}=\frac{\sqrt2+1}{\big(\sqrt2\big)^2-(1)^2}$
$=\frac{\sqrt2+1}{\sqrt2-1}$
$=\sqrt2+1$
Hence the value of the given expresion is $\sqrt2+1.$
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