let a,b be the roots of
x^2 + 3x -7=0
Find without solving the equation the values of
a) a^2 + b^2
b) a^3 +b^3
c)(2a-3b)/a + (2b-3a)/b
help !!!!!!!!!!!!!!
F 4 math
2010-10-12 5:41 am
回答 (1)
2010-10-12 6:16 am
✔ 最佳答案
x^2 + 3x -7=0 a + b = - 3ab = - 7a)a^2 + b^2= (a + b)^2 - 2ab= (- 3)^2 - 2(- 7)= 9 + 14= 23b)a^3 + b^3= (a + b)(a^2 - ab + b^2)= (a + b)(a^2 + 2ab + b^2 - 3ab)= (a + b)[(a + b)^2 - 3ab]= ( - 3)[(- 3)^2 - 3(-7)]= (- 3)(9 + 21)= - 90c)(2a-3b)/a + (2b-3a)/b= [(2ab - 3b^2) + (2ab - 3a^2)] / (ab)= [4ab - 3(a^2 + b^2)] / (ab)= {4ab - 3[(a + b)^2 - 2ab]} / (ab)= {4(-7) - 3[(- 3)^2 - 2(- 7)]} / (- 7)= [- 28 - 3(23)] / - 7= 97/7
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