Question

5 + root 3 by 5 minus root 3 is equal to a + b root 3 find a and b values​

Answer 1

rationalize the denominator

$(5 + \sqrt{3 } ) \div( 5 - \sqrt{3}) =( 5 + \sqrt{3})^{2 } \div ( {5}^{2} - { \sqrt{3} }^{2} ) \\ =( 25 + 3 + 10 \sqrt{3} ) \div( 25 - 3) \\ =( 28 + 10 \sqrt{3}) \div 22 \\ = 14 \div 11 + 5 \sqrt{3} \div 11 \\ therefore \: by \: comparing \: to \: a + b \sqrt{3 } \\ we \: get \: a = 14 \div 11 \: and \: b = 5 \div 11$

${(a + b)}^{2} = {a}^{2} + {b}^{2}. + 2ab \\ and \: (a - b) (a + b) = {a}^{2} - {b}^{2} .$