1.已知x=7/2(√7+√5).y=1/2(√7-√5)求下列各式值.(1)x^2-xy+y^2(2)(x/y)+(y/x)2.计算.(1)√3-√2+{1/(√2+1)}-{2/(√3+1)}(2){5/(4-√11)}+{1/(3+√7)}-{6/(√7-2)}-{(√7-5)/2}(3)(1/y)*√x-y+{x/(√x-y)}-{(1/x-y)}*√(x-y)^2(4)√3÷(

Question

1.已知x=7/2(√7+√5).y=1/2(√7-√5)求下列各式值.
(1)x^2-xy+y^2 (2)(x/y)+(y/x)
2.计算.
(1)√3-√2+{1/(√2+1)}-{2/(√3+1)}
(2){5/(4-√11)}+{1/(3+√7)}-{6/(√7-2)}-{(√7-5)/2}
(3)(1/y)*√x-y+{x/(√x-y)}-{(1/x-y)}*√(x-y)^2
(4)√3÷(√5-√7)-(2√3-5√7)

Answer 1

带入求值:
由题意得：
（1）
x^2-xy+y^2
=(x^2-2xy+y^2)+(xy)[与完全平方公式挂钩,使计算简便]
=(x-y)^2+xy [逆用完全平方公式]
带入数值得:
[7/2(√7+√5)-(1/2(√7-√5))]^2+[(7/2(√7+√5))*(1/2(√7-√5))]
=[(7/2-1/2)(√7+√5)]^2+(7/4)(√7+√5)*(√7-√5)
{逆用乘法分配律}
=[(3)(√7+√5)]^2+(7/4)[(√7)^2-(√5)^2]
{使用平方差公式}
=9(√7+√5)^2+(7/4)(7-5)
=108+18√35+(7/2)
=111.5+18√35
答:为 111.5+18√35
(2)
(x/y)+(y/x)
=(x^2+y^2)/xy [使用分式乘法简便运算]
带入数值为:
{[7/2(√7+√5)]^2+[1/2(√7-√5)]^2}/{[7/2(√7+√5)][1/2(√7-√5)]}
=[(49/4)(√7+√5)^2+(1/4)(√7-√5)^2]/(7/2)
{使用平方差公式}
=[(49/4)(12+2√35)+(1/4)(12-2√35)]/(7/2)
=[147+98√35+3-(√35)/2]
=150+97.5√35
答:为150+97.5√35
计算:
(1)√3-√2+{1/(√2+1)}-{2/(√3+1)}
=√3-√2+√2-1-√3+1
=0
(2){5/(4-√11)}+{1/(3+√7)}-{6/(√7-2)}-{(√7-5)/2}
=4+√11+(3-√7)/2-4-2√7+(√5-7)/2
=4+√11-3√7
(3)(1/y)*√x-y+{x/(√x-y)}-{(1/x-y)}*√(x-y)^2
=√x/y-1+(x√x-y)/x-y^2-)-(1/x-y)*√(x-y)^2
={[xy+x-(√x)y]/[y(√x)-y^2]}-2
(4)√3÷(√5-√7)-(2√3-5√7)
=-√21-√15-2√3-5√7