Question

if one root of x² - x - k = 0 may be the square root of the other root, then k =
1) 2+_ ✓3
2) 3+_ ✓2
3) 2+_ ✓5
4) 5+_ ✓2​

Answer 1

Answer:

Let the roots of the equation be α,α

2

∴α+α

2

=1,α⋅α

2

=−k

⇒(α+α

2

)

3

=1,α

3

=−k

⇒α

3

+α

6

+3α

3

(α+α

2

)=1

now α

3

=−k

⇒−k+k

2

+3(−k)(1)=1

⇒k

2

−4k−1=0

⇒k=

2

4±

16+4

=2±

5