sum & product of the roots

👨🏻‍🏫 學術台數學

rait

2011-02-24 10:56 pm

Given that 2x^2-5x-1=0 has 2 roots : x and y.

Without finding the values of the 2 roots, by using sum & product of the roots, how can we find the values of x^2+y^2 ?

更新1:

Thanks for answering! But I'm a bit confused with the second step. How can x^2+ y^2 -> (x + y)² - 2xy ?

回答 (1)

用戶2053

2011-02-24 11:02 pm

✔ 最佳答案

Sum of roots = x + y = - (-5)/2 = 5/2
Product of roots = - 1/2x² + y²= (x + y)² - 2xy= (5/2)² - 2(- 1/2)= 25/4 + 1= 29/4= 7.25

2011-02-24 15:32:07 補充：
x² + y²

= x² + y² + 2xy - 2xy

= (x² + 2xy + y²) - 2xy

= (x + y)² - 2xy

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