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$Number of integers satisfying \sqrt{8 + 2 x - x^{2}} > 6 - 3 x is$

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Correct option is C

8+2x−x2>6−3x We must have 8+2x−x2≥0⇒ x∈[−2,4]----(1) For 6−3x<0 or x>2 , inequality is satisfied. Let 6−3x≥0⇒ x≤2----(2)⇒ 8+2x−x2>36+9x2−36x⇒ 5x2−19x+14<0⇒ (5x−14)(x−1)<0⇒x∈1,145---(3) From (ii) and (iii), x∈(1,2]∴ finally x∈(1,4]

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The solution of $x - 1 = (x - [x]) (x - {x})$ (where $[x]$ and ${x}$ are the integral and fractional part of $x$ ) is :

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