Question

if alpha and beta are the roots of x^2-(k+1)+1/2(k^2+k+1)=0 then prove that alpha^2 + beta^2=k
​

Answer 1

Answer:

α

2

+β

2

=(α+β)

2

−2αβ

=(k+1)

2

−2×

2

1

(k

2

+k+1)

since

α+β=

a

−b

=k+1;αβ=

a

c

=

2

1

(k

2

+k+1)

=k

2

+2k+1−k

2

−k−1

∴α

2

+β

2

=k

Step-by-step explanation:

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