Question

If x= 2-√3 then x² +4√3 is ?? pls reply fast anybody​

Answer 1

Given x=2−3–√

Find x2−x−2

x2−x−2=x2−1x2

x2=(2−3–√)2=4−43–√+3=7−43–√

x2−x−2=7−43–√−17−43–√

Use the difference of squares trick to rationalize the denominator.

x2−x−2=7−43–√−7+43–√(7−43–√)(7+43–√)

=7−43–√−7+43–√(49−16⋅3)

=7−43–√−7+43–√(49−48)

=7−43–√−(7+43–√)

=7−43–√−7−43–√

=−83–√

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