已知x=√2+√5y=√5-√2求x²+xy=y²和(x+y)²-(x-y)²的值
问题描述:
已知x=√2+√5y=√5-√2求x²+xy=y²和(x+y)²-(x-y)²的值
是x²+xy+y²
答
x²+xy+y²=(√2+√5)²+(√2+√5)(√5-√2)+(√5-√2)²=(√2+√5)²+2(√2+√5)(√5-√2)+(√5-√2)²-(√2+√5)(√5-√2)=[(√2+√5)+(√5-√2)]²-(√5+√2)(√5-√2)=(2√5)²...