Question

Answer my question immediately.
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I need answer for 4th question

Answer 1

Substitute y=1/x in the equation

x²+1/x²+2x×1/x-x×1/x

i.e. (x+1/x)²-1

1/x=1/(4+√15)

Rationalise this,

1/x=(4-√15)/(4²-(√15)²)

1/x=4-√15

So the equation simplifies as

({4+√15}+{4-√15})²-1

=(8)²-1

=64-1=63

Answer 2

(4)

Given x = 4 + √15   ----- (1)

Given xy = 1.  

⇒ y = (1/x)

$= > y = \frac{1}{4 + \sqrt{15}} * \frac{4 - \sqrt{15}}{4 - \sqrt{15}}$

$= > y = \frac{4 - \sqrt{15}}{(4)^2 - (\sqrt{15})^2}$

$= > y = \frac{4 - \sqrt{15}}{16 - 15}$

$= > y = 4 - \sqrt{15}$

Now,

⇒ x^2 + y^2 + xy

⇒ (4 + √15)^2 + (4 - √15)^2 + 1

⇒ 16 + 15 + 8√15 + 16 + 15 - 8√15 + 1

⇒ 31 + 8√15 + 31 - 8√15 + 1

⇒ 62 + 1

⇒ 63.

Therefore, the answer is 63 - Option(3).

Hope this helps!