已知方程ײ-3x+1=0的两个实数根是×₁,×₂,求下列各式的值:﹙1﹚﹙×₁+1﹚﹙×₂+1﹚ ﹙2﹚1/×₁+1/×₂; ﹙3﹚×₁-×₂
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![已知方程ײ-3x+1=0的两个实数根是×₁,×₂,求下列各式的值:﹙1﹚﹙×₁+1﹚﹙×₂+1﹚ ﹙2﹚1/×₁+1/×₂; ﹙3﹚×₁-×₂](/uploads/image/z/1592813-29-3.jpg?t=%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8B%C3%97%26%23178%3B%EF%BC%8D3x%EF%BC%8B1%EF%BC%9D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9%E6%98%AF%C3%97%26%238321%3B%2C%C3%97%26%238322%3B%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%EF%BC%9A%EF%B9%991%EF%B9%9A%EF%B9%99%C3%97%26%238321%3B%EF%BC%8B1%EF%B9%9A%EF%B9%99%C3%97%26%238322%3B%EF%BC%8B1%EF%B9%9A+++++%EF%B9%992%EF%B9%9A1%EF%BC%8F%C3%97%26%238321%3B%EF%BC%8B1%EF%BC%8F%C3%97%26%238322%3B%EF%BC%9B+++++%EF%B9%993%EF%B9%9A%C3%97%26%238321%3B%EF%BC%8D%C3%97%26%238322%3B)
已知方程ײ-3x+1=0的两个实数根是×₁,×₂,求下列各式的值:﹙1﹚﹙×₁+1﹚﹙×₂+1﹚ ﹙2﹚1/×₁+1/×₂; ﹙3﹚×₁-×₂
已知方程ײ-3x+1=0的两个实数根是×₁,×₂,求下列各式的值:
﹙1﹚﹙×₁+1﹚﹙×₂+1﹚ ﹙2﹚1/×₁+1/×₂; ﹙3﹚×₁-×₂
已知方程ײ-3x+1=0的两个实数根是×₁,×₂,求下列各式的值:﹙1﹚﹙×₁+1﹚﹙×₂+1﹚ ﹙2﹚1/×₁+1/×₂; ﹙3﹚×₁-×₂
ײ-3x+1=0
x1+x2=3
x1x2=1
(1)x1x2+x1+x2+1
=1=3+1
=5
(2)1/x1+1/x2
=(x1+x2)/x1x2
=3
(3)(x1-x2)²=(x1+x2)²-4x1x2
=9-4
=5
x1-x2=±√5
1、 负根号5
2、3
3、 根号5
∵x₁,x₂是方程ײ-3x+1=0的两个实数根
∴x₁+x₂=3, x₁·x₂=1
∴﹙1﹚﹙×₁+1﹚﹙×₂+1﹚=x₁x₂+﹙x₁+x₂﹚+1=3+1+1=5
⑵1/×₁+1/...
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∵x₁,x₂是方程ײ-3x+1=0的两个实数根
∴x₁+x₂=3, x₁·x₂=1
∴﹙1﹚﹙×₁+1﹚﹙×₂+1﹚=x₁x₂+﹙x₁+x₂﹚+1=3+1+1=5
⑵1/×₁+1/×₂=﹙x₁+x₂﹚/x₁x₂=3/1=3
⑶ ﹚×₁-×₂=√﹙x₁-x₂﹚²=√[﹙x₁+x₂﹚²-4x₁x₂]=√﹙3²-4×1﹚=√5
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(1)5 (2)3/2 (3)根号5