Find the value of a and b if
Root2+root3/3root2-2root3 =a+b root6
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LHS = ( √2 + √3 )/(3√2-2√3)
= [(√2+√3)(3√2+2√3)]/[(3√2-2√3)(3√2+2√3)]
=[6+2√6+3√6+6]/[(3√2)²-(2√3)²]
= [12+5√6]/[18-12]
= ( 12 + 5√6 )/6
= 12/6 + 5√6/6
= 2 + (5/6)√6 ---( 1 )
= a + b√6-------( 2 )
Compare ( 1 ) and ( 2 ) , we get
a = 2 , b = 5/6
= [(√2+√3)(3√2+2√3)]/[(3√2-2√3)(3√2+2√3)]
=[6+2√6+3√6+6]/[(3√2)²-(2√3)²]
= [12+5√6]/[18-12]
= ( 12 + 5√6 )/6
= 12/6 + 5√6/6
= 2 + (5/6)√6 ---( 1 )
= a + b√6-------( 2 )
Compare ( 1 ) and ( 2 ) , we get
a = 2 , b = 5/6
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