If a^2 + 6a - 1 = 0, then what is the value of (a+\frac{1}{a})^{2}-5(a-\frac{1}{a})?

CAT 2016 Quantitative Ability

Question : 9 of 34

Marks: +1, -0

a^2 + 6a - 1 = 0

, then what is the value of

(a+{1}/{a})^{2}-5(a-{1}/{a})?

Solution:

a^{2}-1=-6a

⇒

a-\;\;{1}/{a}=-6

Now,

(a+\;\;{1}/{a})^{2}-5(a-\;\;{1}/{a})

=((a-\;\;{1}/{a})^{2}+4) -5(a-\;\;{1}/{a})

=((-6)^{2}+4)-5×-6

=40 + 30 = 70.

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