Posted by **njovu** on Tuesday, March 13, 2012 at 7:40am.

Given that the roots of 2x^2-4x+5 are alpha and beta,find the value of ...

(i)alpha^3beta^3

(ii)(alpha-beta)^2

- maths -
**Reiny**, Tuesday, March 13, 2012 at 8:33am
Using the sum and product of roots property, we know

a+b = - (-4/2) = 2 and ab = 5/2, where a and b are alpha and beta

we know that

(a+b)^3 = a^3 + b^3 + 3a^2b + 3ab^2

(a+b)^3 = a^3 + b^3 + 3ab(b+a)

2^3 = a^3 + b^3 + 3(5/2)(2)

8 = a^3 + b^3 + 15

a^3 + b^3 = -7

in the same way....

(a-b)^2 = a^2 - 2ab + b^2

= a^2 +b^2 - 2ab

but a^2 + b^2 = (a+b)^2 - 2ab

so

(a=b)^2 = (a+b)^2 - 2ab - 2ab

= 4 - 5/2 - 5/2

= -1

- silly typo - maths -
**Reiny**, Tuesday, March 13, 2012 at 10:20am
in the third last line I should have had

(a-b)^2 = (a+b)^2 - 2ab - 2ab

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