CMAT 2016 Solved Question Paper

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Question : 9 of 100

Marks: +1, -0

If a and p are the roots of the equation

x^2

-16x + 1 =0, then the value of the following expression is

(1/α-16)^2 + (1/β - 16)^2

194
254
226
264

Solution:

(b)

x^2

-16x + 1 =0,
⇒ x =

{16 ± √{256 - 4 × 1 × 1}/2

⇒ x =

{16 ± 2√63}/2

⇒ x = 8 ±

√63

Let α = 8 +

√63

and β = 8 -

√63

Then

1/α

=

{8 - √63}/{(8 + √63)(8 - √63)

= 8 -

√63

and

1/β

=

{8 + √63}/{(8 - √63)(8 + √63)

= 8 +

√63

Now,

(1/α-16)^2 + (1/β - 16)^2

=

(8 - √63 - 16)^2

+

(8 + √63 - 16)^2

=

(- √63 - 8)^2

+

( √63 - 8)^2

= 63 + 64 + 16

√63

+ 63 + 64 - 16

√63

= 126 + 128 + = 254

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