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Equation 3√[−2(x+3)] −1=|x+3|+a has exactly two real roots , then the maximum possible value of |[a]| is _________. { where [.] denotes the greatest integer function } . |
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Answer» \(3\sqrt{[-2(x +3)] - 1} = |x + 3| + a\) For existence \([-2(x + 3)] - 1 \ge 0\) ⇒ \([-2(x +3)] \ge 1\) ⇒ \(-2(x + 3) \ge 1\) ⇒ \(x + 3 \le \frac{-1}2\) ⇒ \(x \le \frac {-1}2 -3\) ⇒ \(x \le \frac{-5}2\) Also \(|x + 3| \ge \frac 12\) \(|x + 3| + a \ge \frac 12 + a\) |
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