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Various root solutions, equation matching methods, formula methods and calculation problems are solved as follows.
√6-√ 1/2×√ 24+2 √ 2/3.

=(√6-√2/2)×(2√6+2√6/3)

=(√6-√2/2)×(8√6/3)

=(8×6)/3-(√2/2)×(8√6/3)

= 16-8√3/3

√8+√32+√ 18-√24

=2√2+4√2+3√2-2√6

=9√2-2√6

2x? + 1=-(4x? -2x-5)

2x? + 1+4x? -2x-5=0

6x? -2x-4=0

3x? -x-2=0

(x- 1)(3x+2)=0

So x= 1 or x=-2/3.

2√ 12+3√ 1 you 1/3-5 you 1/3-2/3√48

=4√3+√2 1-4√3/3-8√3/3

=4√+√2 1-4√3

=√2 1

(2√ 12-3√ one sixth) ×√6

=(4√3-√6/2)×√6

= 12√2-3

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