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(3 + √5)/(2√5 + 3) = a + b√5find a and b |
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Answer» ,LHS = ( 3 - √5 )/(3 + 2√5 )Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )= ( 9√5 - 19 )/11Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )= ( 9√5 - 19 )/11= ( 9/11 )√5 - 19/11 ---( 1 )Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )= ( 9√5 - 19 )/11= ( 9/11 )√5 - 19/11 ---( 1 )= a√5 - b ----------( 2 ) [ RHS ]Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )= ( 9√5 - 19 )/11= ( 9/11 )√5 - 19/11 ---( 1 )= a√5 - b ----------( 2 ) [ RHS ]from ( 1 ) and ( 2 ) ,Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )= ( 9√5 - 19 )/11= ( 9/11 )√5 - 19/11 ---( 1 )= a√5 - b ----------( 2 ) [ RHS ]from ( 1 ) and ( 2 ) ,a = 9/11 ,Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )= ( 9√5 - 19 )/11= ( 9/11 )√5 - 19/11 ---( 1 )= a√5 - b ----------( 2 ) [ RHS ]from ( 1 ) and ( 2 ) ,a = 9/11 ,b = 19/11Hi ,LHS = ( 3 - √5 )/(3 + 2√5 )= [(3-√5)(2√5-3)]/[(2√5+3)(2√5-3)]= [6√5 - 9 -10 + 3√5 ]/[ ( 2√5 )² - 3² ]= ( 9√5 - 19 )/( 20 - 9 )= ( 9√5 - 19 )/11= ( 9/11 )√5 - 19/11 ---( 1 )= a√5 - b ----------( 2 ) [ RHS ]from ( 1 ) and ( 2 ) ,a = 9/11 ,b = 19/11I hope this HELPS you. |
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