Log по основанию x+1 числа x^2-x-2≤1

Question

Log по основанию x+1 числа x^2-x-2≤1

Математика

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Accepted Answer

Logₓ₊₁ x²-x-2≤1 00 -10 x²-x-2-x-1≥0, x²-2x-3≥0 D=4+4·3=16, √D=4, x ₁=(2+4)/3=3, x₂=(2-4)/2=-1 (x-3)(x+1)≥0 + - - + ---------------------- -1--------------------0---------------2------3------>x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\ x∈∅ x>0 (x+1)(x-2)>0 x²-2x-3≤0 ,(x+1)(x-3)≤0 ////////////////////////////// //////////////////////////////////////////// --------------------- -1 -------------0---------------2--------------3------------------->x ///////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ x∈(2;3]