. If a =
√3 − √2
√3 + √2
and b =
√3 + √2
√3 − √2
, then find the value of a
2 + b2
– 5ab.
Answers
Answered by
16
a=√3-√2/√3+√2
=(√3-√2)2/(√3)2-(√2)2
=3+2-2√6/3-2
=5-2√6
a2=(5-2√6)2
=25+24-20√6
=49-20√6
b=√3+√2/√3-√2
=(√3+√2)2/(√3)2-(√2)2
=3+2+2√6/3-2
=5+2√6
b2=(5+2√6)2
=25+24+20√6
=49+20√6
ab=(5-2√6)(5+2√6)
=52-(2√6)2
=25-24
=1
a2+b2-5ab=49-20√6+49+20√6-5*1
=98-5
=93
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