第1个回答 2010-08-20
1.(x-5)^2=2(x-5)
(x-5)^2-2(x-5)=0
(x-5)(x-5-2)=0
(x-5)(x-7)=0
x=5,x=7
2.x^2-(√2)*x-1/4=0
x^2-√2x+1/2=1/4+1/2=3/4
(x-√2/2)^2=(±√3/2)^2
x-√2/2=±√3/2
x=(√2+√3)/2,x=(√2-√3)/2
3.x^2+(22√5)*x+10=0
x^2+22√5x+(11√5)^2=-10+(11√5)^2=595
(x+11√5)^2=(±√595)^2
x+11√5=±√595
x=-11√5+√595,x=-11√5-√595
4.已知a,b是方程x^2+x-1=0的两根,求a^2+2a+1/b的值
a是方程的根
所以a^2+a-1=0
a^2+a=1
a^2+2a=a^2+a+a=a+1
所以a^2+2a+1/b=a+1+1/b=(ab+b+1)/b
由韦达定理，ab=-1
所以a^2+2a+1/b=(ab+b+1)/b=(-1+b+1)/b=b/b=1
第3个回答 2010-08-20
^2是平方的意思！
①5√8-2√32+√50
=5*3√2-2*4√2+5√2
=√2(15-8+5)
=12√2
②√6-√3/2-√2/3
=√6-√6/2-√6/3
=√6/6
③(√45+√27)-(√4/3+√125)
=(3√5+3√3)-(2√3/3+5√5)
=-2√5+7√5/3
④(√4a-√50b)-2(√b/2+√9a)
=(2√a-5√2b)-2(√2b/2+3√a)
=-4√a-6√2b
⑤√4x*(√3x/2-√x/6)
=2√x(√6x/2-√6x/6)
=2√x*(√6x/3)
=2/3*|x|*√6
⑥(x√y-y√x)÷√xy
=x√y÷√xy-y√x÷√xy
=√x-√y
⑦(3√7+2√3)(2√3-3√7)
=(2√3)^2-(3√7)^2
=12-63
=-51
⑧(√32-3√3)(4√2+√27)
=(4√2-3√3)(4√2+3√3)
=(4√2)^2-(3√3)^2
=32-27
=5
⑨(3√6-√4)2
=(3√6)^2-2*3√6*√4+(√4)^2
=54-12√6+4
=58-12√6
⑩（1+√2-√3）（1-√2+√3）
=[1+(√2-√3)][1-(√2-√3)]
=1-(√2-√3)^2
=1-(2+3+2√6)
=-4-2√6