6
Question
Simplify √6√2+√3+3√2√6+√3−4√3√6+√2.
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Solution
√6√2+√3+3√2√6+√3−4√3√6+√2
=√6(√2−√3)(√2+√3)(√2−√3)+3√2(√6−√3)(√6+√3)(√6−√3)−4√3(√6−√2)(√6−√2)(√6+√2)
=√6(√2−√3)(√2+√3)(√2−√3)+3√2(√6−√3)(√6+√3)(√6−√3)−4√3(√6−√2)(√6−√2)(√6+√2)
=√12−√182−3+3√12−3√66−3−(4√18−4√6)6−2
=2√3−3√2−1+6√3−3√63−(12√2−4√6)4
=3√2−2√3+2√3−√6−3√2+√6
=0
√6√2+√3+3√2√6+√3−4√3√6+√2
=√6(√2−√3)(√2+√3)(√2−√3)+3√2(√6−√3)(√6+√3)(√6−√3)−4√3(√6−√2)(√6−√2)(√6+√2)
=√6(√2−√3)(√2+√3)(√2−√3)+3√2(√6−√3)(√6+√3)(√6−√3)−4√3(√6−√2)(√6−√2)(√6+√2)
=√12−√182−3+3√12−3√66−3−(4√18−4√6)6−2
=2√3−3√2−1+6√3−3√63−(12√2−4√6)4
=3√2−2√3+2√3−√6−3√2+√6
=0
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