Question

If α and β are zeroes of 2x2

-5x +3 then find value of (i) α2 +β2



(ii)1/2α+1/2β

(iii)α/β+β/α (iv)α3+β3

Answer 1

here is your answer by Sujeet,

Given that polynomial,
2x²-5x+3
sum of zeroes=-b/a=-(-5)/2=5/2
product of zeroes=c/a=3/2

then,
value of
(1)

a²+b²
(a+b)²-2ab
(5/2)²-2*3/2
25/4-3/1
25-12/4
13/4

(2)


1/2a+/2b
2b+2a/4ab
2(a+b)/4ab
2(5/2)/4*3/2
2*5/2 / 2*3
5/6

(3)



a/b+b/a

a+b/ab
5/2 / 3/2
5/3


(4)


a³+b³

(a+b)(a²+b²-2ab)
(a+b){(a²+b²}
(a+b)((a+b)²-2ab
(5/2) (5/2)²-2*3/2
(5/2)(25/4)-3
5/2*25/4 -3
125/8-24/1
101/8




that's all......


I'm confused in last question....




that's all

Answer 2

solution: a²+b²

(a+b) - 2ab

(5/2)²-2*3/2

25/4-3/1