Home » Aptitude » Algebra » Question
  1. If   a =
    1
    (a > 0), then the value of a +
    1
    is
    a − 5a
    1. 29
    2. −√27
    3. −√29
    4. 27
Correct Option: A

a =
1
a – 5

⇒  a2 – 5a = 1
⇒  a2 – 5a – 1 = 0
∴  a =
5 ± √(−5)² − 4 × 1 × (−1)
2

If ax² + bx + c = 0, then x =
−b ± √(b)² − 4ac
2a

=
5 ± √25 + 4
2

=
5 ± √29
2

If   a =
5 ± √29
,   then
2

1
=
2
a5 + √29

2
×
5 − √29
5 + √295 − √29

=
2(5 − √29)
=
5 − √29
25 − 29−2

∴  a +
1
=
5 + √29
5 − √29
a22

=
5 + √29 − 5 + √29
= √29
2



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