Question

$\sqrt{3 - x { }^{2} + 2x }^{2} = x {}^{2} + \frac{1}{x {}^{2} } for \: real \: value \: of \: x \:$
the fore sent value of the​

Answer 1

Answer:

x

2

+2x+2=0

Here, a=1,b=2,,c=2

From quadratic formula,

x=

2×1

−2±

2

2

−4×2×1

⇒x=

2

−2±2i

=−1±i

Therefore,

α=−1+i⇒α

2

=(−1+i)

2

=−2i

β=−1−i⇒β

2

=(−1−i)

2

=2i

Now,

α

15

+β

15

=(α

2

)

7

⋅α+(β

2

)

7

⋅β

=(−2i)

7

(−1+i)+(2i)

7

(−1−i)

=(−2)

7

(−i)(−1+i)+2

7

(−i)(−1−i)

=2

7

i(−1+i)+2

7

i(1+i)

=2

7

i(−1+i+1+i)

=2

7

i⋅2i

=2

8

⋅(−1)

=−256