Solutions of the equation x - x - 1 - - 1 - 0 are i 1 - 2 1 - 5 ii - 1 - 2 - 1 - 5 iii 1 - 2 - 1 - - 5

x| x+1 | +1=0 x(x+1)+1=0 x( x 1)+1=0 x ^ 2 +x+1=0 x ^ 2 x+1=0 x= 1±√( 1 4 ) #160; 2 x= ...

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Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

Solutions of ...

Question

Solutions of the equation $x | x + 1 | + 1 = 0$ are
(i) $\frac{1}{2} (1 \pm \sqrt{5})$
(ii) $\frac{- 1}{2} (- 1 \pm \sqrt{5})$
(iii) $\frac{1}{2} (- 1 + \sqrt{5})$

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Solution

$x | x + 1 | + 1 = 0 x (x + 1) + 1 = 0 x (- x - 1) + 1 = 0 x^{2} + x + 1 = 0 - x^{2} - x + 1 = 0 x = \frac{- 1 \pm \sqrt{1 - 4}}{2} x = \frac{- 1 \pm \sqrt{1 + 4}}{2} = \frac{- 1 \pm \sqrt{3} i}{2} = \frac{- 1 \pm \sqrt{5}}{2} ∴ x = - \frac{1}{2} (1 \pm \sqrt{5})$

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Similar questions

Q. Solve the matrix equations:
(i)

[x 1] [\begin{matrix} 1 & 0 \\ - 2 & - 3 \end{matrix}] [\begin{matrix} x \\ 5 \end{matrix}] = 0

(ii)

[1 2 1] [\begin{matrix} 1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{matrix}] [\begin{matrix} 0 \\ 2 \\ x \end{matrix}] = 0

(iii)

[x - 5 - 1] [\begin{matrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{matrix}] [\begin{matrix} x \\ 4 \\ 1 \end{matrix}] = 0

In each of the following, determine whether the given values are solutions (roots) of the equation or not :
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(iii) $x^{2} + x - 4 = 0$ ; x = – 2

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i.

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ii.

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How many of the following are quadratic equation?

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Q. If

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Solutions of the equation x|x+1|+1=0 are (i) 12(1±√5)(ii) −12(−1±√5)(iii) 12(−1+√5)

x|x+1|+1=0x(x+1)+1=0x(−x−1)+1=0x2+x+1=0−x2−x+1=0x=−1±√1−42x=−1±√1+42=−1±√3i2=−1±√52∴x=−12(1±√5)

Solutions of the equation $x | x + 1 | + 1 = 0$ are
(i) $\frac{1}{2} (1 \pm \sqrt{5})$
(ii) $\frac{- 1}{2} (- 1 \pm \sqrt{5})$
(iii) $\frac{1}{2} (- 1 + \sqrt{5})$

$x | x + 1 | + 1 = 0 x (x + 1) + 1 = 0 x (- x - 1) + 1 = 0 x^{2} + x + 1 = 0 - x^{2} - x + 1 = 0 x = \frac{- 1 \pm \sqrt{1 - 4}}{2} x = \frac{- 1 \pm \sqrt{1 + 4}}{2} = \frac{- 1 \pm \sqrt{3} i}{2} = \frac{- 1 \pm \sqrt{5}}{2} ∴ x = - \frac{1}{2} (1 \pm \sqrt{5})$