Question

若方程|X^2-2X-3|=K+2X 有三个或三个以上的解,求K的取值范围

Answer 1

|(X+1)(X-3)|=|X^2-2X-3|=K+2X≥0,X≥-K/2 ①当X≤-1或X≥3时,X^2-2X-3=K+2X,X^2-4X-(K+3)=0,0≤⊿=4^2+4(K+3)=4(K+7),K≥-7 -1≥X≥-K/2,K≥2.②当-1≤X≤3时,-(X^2-2X-3)=K+2X,3-K=X^2≥0,K≤3 ∴2≤K≤3