Question

Prove that: [4+3-√20]^2/2+[4-3-√20]^1/2 = 6.​

Answer 1

Answer:

Let x+iy=

4+3

20

i

∴(x+iy)

2

=4+3

20

i

expanding ,

x

2

+2ixy−y

2

=4+3

20

i

equating real & imaginary parts

x

2

−y

2

=4−−−−−−−−−−−(1)

2xy=3

20

−−−−−−−−−−−−−−−−(2)

By equaling the modules

∣

∣

∣

(x+iy)

2

∣

∣

∣

=

∣

∣

∣

4+3

20

i

∣

∣

∣

∴x

2

+y

2

=

4

2

+(3

20

)

2

=

16+180

=

196

=14

∴x

2

+y

2

=14−−−−−−−−−−(3)