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Question
Complete solution set of ∣∣x2−5x+7∣∣+∣∣x2−5x−14∣∣=21 is -
Complete solution set of ∣∣x2−5x+7∣∣+∣∣x2−5x−14∣∣=21 is -
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Solution
The correct option is A [−2,7]
|a|+|b|=|a−b|
After squaring on both sides we get,
⇒|a||b|=−ab
⇒ab≤0
(x2−5x+7)(x2−5x−14)≤0
Here, x2−5x+7>0 ∀ x∈R
⇒x2−5x−14≤0
⇒(x−7)(x+2)≤0
⇒x ∈ [−2,7]
|a|+|b|=|a−b|
After squaring on both sides we get,
⇒|a||b|=−ab
⇒ab≤0
(x2−5x+7)(x2−5x−14)≤0
Here, x2−5x+7>0 ∀ x∈R
⇒x2−5x−14≤0
⇒(x−7)(x+2)≤0
⇒x ∈ [−2,7]
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