Question

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

Answer 1

Step-by-step explanation:

a = (√3-√2)/(√3+√2)

  = (√3-√2)/(√3+√2)× (√3-√2)/(√3-√2) [ rationalizing it]

  =(√3 -√2)²/1 = (√3 -√2)² = 5- 2√6

b= (√3+√2)/(√3-√2)×(√3+√2)/(√3+√2) [ rationalizing it]

 = (√3+√2)²/1 =(√3+√2)² = 5+2√6

now, a²+b² - 5ab 

= (5-2√6)² + (5+2√6)² - 5(5-2√6)(5+2√6)

=25 +24 -20√6 +25 +24 + 20√6 - 5(25-24)

=98 -5 = 93

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