9514 1404 393
Answer:
(vii) 25/4
(ix) -61/6
Step-by-step explanation:
(vii) Once again, we remind you that for ax²+bx+c=0, ...
α+β = -b/a = -(-7/2) = 7/2 = 3.5
αβ = c/a = -3/2 = -1.5
Then the desired expression is ...
α/(β+1) +β/(α+1) = (α² +α +β² +β)/((α+1)(β+1))
= ((α+β)² -2αβ +(α+β))/(αβ +(α+β) +1)
= (3.5² -2(-1.5) +3.5)/(-1.5 +3.5 +1) = 18.75/3 = 6.25 = 25/4
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(ix) α/β +β/α = (α²+β²)/(αβ)
= ((α+β)² -2αβ)/(αβ) = (3.5² -2(-1.5))/-1.5 = 15.25/-1.5 = -61/6
