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Polynomial Expressions

If x=2-1, the...

Question

If x= $\sqrt{2} - 1$ , then write the value of $\frac{1}{x} .$

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Solution

Given that.Hence is given as

We know that rationalization factor for is . We will multiply each side of the given expression by, to get

Hence the value of the given expression is.

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∣ ∣ ∣ \begin{matrix} x + 1 & x - 1 x - 3 & x + 2 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 1 & - 1 1 & 3 \end{matrix} ∣ ∣ ∣

, then write the value of

x

[\begin{matrix} x + 1 & x - 1 x - 3 & x + 2 \end{matrix}] = [\begin{matrix} 4 & - 1 1 & 3 \end{matrix}]

, then write the value of

x

|\begin{matrix} x + 1 & x - 1 \\ x - 3 & x + 2 \end{matrix}| = |\begin{matrix} 4 & - 1 \\ 1 & 3 \end{matrix}|

, then write the value of x.

y = \sec^{- 1} (\frac{x + 1}{x - 1}) + \sin^{- 1} (\frac{x - 1}{x + 1})

, then write the value of

\frac{d y}{d x} .

|\begin{matrix} 2 x & x + 3 \\ 2 (x + 1) & x + 1 \end{matrix}| = |\begin{matrix} 1 & 5 \\ 3 & 3 \end{matrix}|

, then write the value of x.

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