已知关于x的方程x²﹣（k+1）x+$\frac{1}{4}$k²+1=0有两个实数根．

（1）求k的取值范围；

（2）若方程的两实数根分别为x₁、x₂，且满足|x₁|+|x₂|=4x₁x₂﹣5，求k的值．

阅读理解

    Everyone gathered around and Paddy read out loud, slowly, his tone growing sadder and sadder. The little headline said: BOXER RECEIVES LIFF SENTENCE.

    Frank Cleary, aged 26, professional boxer, was today found guilty of the murder of Albert Gumming, aged 32, laborer, last July. The jury(陪审团) reached its decision after only ten minutes, recommending the most severe punishment to the court. It was, said the Judge, a simple case. Cumming and Cleary had quarreled violently at the Harbour Hotel on July 23rd and police saw Cleary kicking at the head of the unconscious Gumming. When arrested, Cleary was drunk but clear-thinking.

    Cleary was sentenced to life imprisonment with hard labour. Asked if he had anything to say, Cleary answered, “Just don't tell my mother.”

    “It happened over three years ago,” Paddy said helplessly. No one answered him or moved, for no one knew what to do. “Just don't tell my mother,” said Fee numbly(麻木地). “And no one did! Oh, God! My poor, poor Frank!”

    Paddy wiped the tears from his face and said. “Fee, pack your things. We'll go to see him.”

    She half-rose before sinking back, her eyes in her small white face stared as if dead. “I can't go,” she said without a hint of pain, yet making everyone feel that the pain was there. “It would kill him to see me. I know him so well—his pride, his ambition. Let him bear the shame alone, it's what he wants. We've got to help him keep his secret. What good will it do him to see us?”

    Paddy was still weeping, not for Frank, but for the life which had gone from Fee's face, for the dying in her eyes. Frank had always brought bitterness and misfortune, always stood between Fee and himself. He was the cause of her withdrawal from his heart and the hearts of his children. Every time it looked as if there might be happiness for Fee, Frank took it away. But Paddy's love for her was as deep and impossible to wipe out as hers was for Frank.

    So he said, “Well, Fee, we won't go. But we must make sure he is taken care of. How about if I write to Father Jones and ask him to look out for Frank?”

    There was no excitement in the eyes, but a faint pink stole into her cheeks. “Yes, Paddy, do that. Only make sure he knows not to tell Frank we found out. Perhaps it would ease Frank to think for certain that we don't know.”