If a and b are the roots of the equation x^2-2x-1=0, form an equation with roots a+2b and b+2a.
PLz show the steps.
x^2-2x-1=0
2007-11-06 4:51 am
回答 (2)
2007-11-06 5:00 am
✔ 最佳答案
a+b = 2 , ab = -1Sum of required roots = a+2b+b+2a = 3(a+b) = 6
Product of required roots = (a+2b)(b+2a) = 5ab + 2(a^2 + b^2)
= 2(a^2 + 2ab + b^2) + ab
= 2(a+b)^2 + ab
= 2(2)^2 - 1
= 7
Required equation:
x^2 - 6x + 7 = 0
2007-11-06 5:11 am
a+b=2
ab=-1
sum of root:a+2b+b+2a
=a+b+2(a+b)
=2+2(2)
=6
product of root;(a+2b)(b+2a)
=ab+2a^2+2b^2+4ab
=5ab+2(a^2+b^2)
=5ab+2(a^2+2ab+b^2-2ab)
=5ab+2[(a+b)^2-2ab]
=5ab+2(a+b)^2-4ab
=ab+2(a+b)^2
=-1+2(2)^2
=7
The equation is:x^2-6x+7=0.
ab=-1
sum of root:a+2b+b+2a
=a+b+2(a+b)
=2+2(2)
=6
product of root;(a+2b)(b+2a)
=ab+2a^2+2b^2+4ab
=5ab+2(a^2+b^2)
=5ab+2(a^2+2ab+b^2-2ab)
=5ab+2[(a+b)^2-2ab]
=5ab+2(a+b)^2-4ab
=ab+2(a+b)^2
=-1+2(2)^2
=7
The equation is:x^2-6x+7=0.
收錄日期: 2021-04-13 18:12:07
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