Why #3x^2+3/x^2=3(x+1/x)^2-6?#

Question

How did we get 6?
#3(x+1/x)^2-6=9x^2+9+9/x^2-6=9x^2+3+9/x^2=3x^2+3/x^2#

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Answer 1 · 2018-06-16T13:07:04

See the proof below

By the binomial Formula

#(a+b)^2=a^2+2ab+b^2#
we get

#3(x^2+1/x^2+2*x*1/x)-6=3(x^2+1/x^2)+6-6=3(x^2+1/x^2)#

Answer 2 · 2018-06-16T13:09:27

Please see below.

#3x^2+3/x^2#

= #3(x^2+1/x^2)#

= #3(x^2+2×x×1/x+(1/x)^2-2×x×1/x)#

= #3((x+1/x)^2-2)#

= #3(x+1/x)^2-6#

Answer 3 · 2018-06-16T13:11:14

#3(x+1/x)^2 - 6#

#3(x^2+1/x^2+2)-6#

Open the brackets,

#3x^2+3/x^2+6-6#

#3x^2+3/x^2#