If x3-x2-x-1x3-x2-x-1-x2-x-1x2-x-1- then the number of real-value of x satisfying are

The correct option is B 0Given that x^3+x^2+x+1x^3 x^2+x+1=x^2+x+1x^2 x+1 Performing Componendo Dividendo, we get ⇒x^3+x^2+x+1+x^3 x^2+x+1x^3+x^2+x+1 x ...

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Byju's Answer

Standard X

Mathematics

Componendo and Dividendo

If x3+x2+x+...

Question

If $\frac{x^{3} + x^{2} + x + 1}{x^{3} - x^{2} + x - 1} = \frac{x^{2} + x + 1}{x^{2} - x + 1}$ , then the number of real-value of $x$ satisfying are

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Solution

The correct option is B 0
Given that

$\frac{x^{3} + x^{2} + x + 1}{x^{3} - x^{2} + x + 1} = \frac{x^{2} + x + 1}{x^{2} - x + 1}$

Performing Componendo Dividendo, we get

$\Rightarrow \frac{x^{3} + x^{2} + x + 1 + x^{3} - x^{2} + x + 1}{x^{3} + x^{2} + x + 1 - x^{3} + x^{2} - x + 1} = \frac{x^{2} + x + 1 + x^{2} - x + 1}{x^{2} + x + 1 - x^{2} + x - 1}$

$\Rightarrow \frac{2 x^{3} + 2 x}{2 x^{2} + 2} = \frac{2 x^{2} + 2}{2 x}$

$\Rightarrow \frac{x^{3} + x}{x^{2} + 1} = \frac{x^{2} + 1}{x}$

$\Rightarrow x (x^{3} + x) = (x^{2} + 1)^{2}$

$\Rightarrow x^{4} + x^{2} = x^{4} + 1 + 2 x^{2}$

$\Rightarrow x^{2} = - 1$

Hence no real values of $x$ satisfy this equation.

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