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If the set of values of x satisfying the equation [2 x]+[-2 x]= ₁₀ (x^2-2 x+2 )-1 | ₁₀ (x^2-2 x+2 )-1 | is; (a, b)- p₁, p₂, , p_n , then find the value of (a+b+ _ i=1 ^n p_i ) . [Note: [k] denotes greatest integer function less than or equal to k .]

Correct answer

13

Step-by-step solution

aligned & ₁₀ (x^2-2 x+2 )-1 10 & x^2-2 x-8 < 0 x (-2,4) & 2 x I x -3 2 ,-1, -1 2 , 0, 1 2 , 1, 3 2 , 2, 5 2 , 3, 7 2 & x (-2,4)- 3 2 , 1 2 , 1,0,2, 5 2 , 3, 7 2 & (a+b+ _ i=1 ^n p_l )=-2+4+5+6=13 aligned

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