√3+√2/√3-√2=a+b√6
find the value of a and b
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Step-by-step explanation:
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Step-by-step explanation:
√3 + √2/√3 - √2 = a + b√6
first we will rationalise √3 + √2/√3 - √2
in order to rationalise the denominator we will multiply √3 + √2
√3 + √2 × √3 + √2/ √3 - √2 × √3 + √2
( √3 + √2 )²/ (√3)² - (√2)²
using (a + b)² = a² + b² + 2ab in numerator
and using a² - b² = (a + b)(a - b) in denominator
(√3)² + (√2)² + 2(√3)(√2)/ 3 - 2
3 + 2 + 2√6/1 = a + b√6
5 + 2√6 = a + b√6
therefore ,
a = 5
b = 2
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