Question

If a=√3-√2/√3+√2 and b=√3+√2/√3-√2 find the value of a²+b²-5ab

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Answer 1

Answer:

93

Step-by-step explanation:

a=√3-√2/√3+√2

=(3-√2/√3+√2)(3-√2/√3-√2)

=(√3-√2)^2/(√3+√2)(√3-√2)

=(3+2-2√6)/3-2[in numerator using identity( a-b)^2=a^2-2ab+b^2 and in denominator using identity (a+b)(a-b)= a^2-b^2]

a=5-2√6

b=√3+√2/√3-√2

=(3+√2/√3-√2)(3+√2/√3+√2)

=(√3+√2)^2/(√3+√2)(√3-√2)

=(3+2+2√6)/3-2[in numerator using identity( a+b)^2=a^2+2ab+b^2 and in denominator using identity (a+b)(a-b)= a^2-b^2]

b=5+2√6

a^2+b^2-5ab

=(5-2√6)^2+(5+2√6)^2-5(5-2√6)(5+2√6)

=25-20√6+24+25+20√6+24-[5(5^2-(2√6)^2)]

=98-[5(25-24)]

=98-5

=93