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Answer:-
x² - 4x + 2 = 0
Now,
α + β = 4 ••••• (i)
αβ = 2 •••••• (ii)
From (i)
β = 4 - α ••••• (iii) put in (ii)
α ( 4 - α ) = 2
α² - 4α + 2 = 0
Now we have a quadratic equation, so we will solve it
α = -b ± √ b² - 4ac / 2a
= 4 ± 2√2 /2
We will take any one value so lets take α = 4 - 2√2 / 2
Rationalizing this we get,
α = 1/3 •••••• (iv) put in (iii)
β = 4 - 1/3
β = 11/3
Now,
( α + 1 )-² + ( β + 1 )-²
= (4/3)-² + 4-²
= 16/9 - 16
= -128/9
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