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4-2.Quadratic Equations and Inequations
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સમીકરણ $|x - 2|^2 + |x - 2| - 6 = 0$ નાં બીજ ......છે.
A
$0, 4$
B
$-1, 3$
C
$4, 2$
D
$5, 1$
Solution
જ્યારે $ \,x < 2,$ ${(x – 2)^2} – (x – 2) – 6 = 0$
$ \Rightarrow {x^2} – 4x + 4 – x + 2 – 6 = 0$
$ \Rightarrow \,\,{x^2} – 5x = 0$
$ \Rightarrow \,\,x(x – 5) = 0$ $ \Rightarrow \,\,x = 0$
જ્યારે $,\,x \ge 2\,;$ ${(x – 2)^2} + (x – 2)\, – 6 = 0$
$ \Rightarrow {x^2} – 4x + 4 + x – 2 – 6 = 0$
$ \Rightarrow \,\,{x^2} – 3x – 4 = 0$
$ \Rightarrow \,\,{x^2} – 4x + x – 4 = 0$
$ \Rightarrow \,(x – 4)(x + 1) = 0$
$ \Rightarrow \,x = 4$
Standard 11
Mathematics
