Question

If alpha, beeta be the roots of 2x² - 4x - 1 = 0 find the value of—
1. (alpha-beeta)^2
2. (alpha^2/beeta) + (beeta^2/alpha)

[Maths Class 10]

Please help me with this question.​

Answer 1

Answer:

(

(α+2β)

1

+

(β+2α)

1

)=

(α+2β)(β+2α)

β+2α+2β+α

=

αβ+2β

2

+2α

2

+4αβ

3(α+β)

=

5αβ+2(α

2

+β

2

)

3(α+β)

=

5αβ+2((α+β)

2

−2αβ)

3(α+β)

=

2(α+β)

2

+αβ

3(α+β)

→(I)

Since α,β are the roots of 2x

2

−4x+1=0,

Sum of the roots =α+β=−

a

b

=−(−4)/2=2 →(II)

Product of the roots =αβ=

a

c

=1/2 →(III)

Substituting (II),(III) in (I),

(

(α+2β)

1

+

(β+2α)

1

)=

2(2)

2

+

2

1

3×2

=

8−

2

1

6

=

16+1

12

=

17

12