(1)已知x+y=12,xy=9,且x>y,求x12-y12x12+y12的值.(2)lg25+23lg8+lg5•lg20+(lg2)2.-数学

题目简介

(1)已知x+y=12,xy=9,且x>y,求x12-y12x12+y12的值.(2)lg25+23lg8+lg5•lg20+(lg2)2.-数学

题目详情

(1)已知x+y=12,xy=9,且x>y,求
x
1
2
-y
1
2
x
1
2
+y
1
2
的值.
(2)lg25+
2
3
lg8+lg5•lg20+(lg2)2
题型:解答题难度:中档来源:不详

答案

(1)∵x+y=12,xy=9,且x>y,
xclass="stub"1
2
-yclass="stub"1
2
xclass="stub"1
2
+yclass="stub"1
2
>0
且(
xclass="stub"1
2
-yclass="stub"1
2
xclass="stub"1
2
+yclass="stub"1
2
)2=
x+y-2(xy)class="stub"1
2
x+y+2(xy)class="stub"1
2
=class="stub"12-6
12+6
=class="stub"1
3

xclass="stub"1
2
-yclass="stub"1
2
xclass="stub"1
2
+yclass="stub"1
2
=
3
3

(2)lg25+class="stub"2
3
lg8+lg5•lg20+(lg2)2

=lg25+lg4+lg5•lg20+(lg2)2
=2+(1-lg2)•(1+lg2)+(lg2)2
=2+1
=3

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