If( 7+3√5/3+√5)-(7-3√5/3-√5)=a+b√5 then find a and b
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Hi ,
LHS = [ (7+3√5)/(3+√5)]-[(7-3√5)/(3-√5)]
=[(7+3√5)(3-√5)-(7-3√5)(3+√5)]/[(3+√5)(3-√5)]
= [21-7√5+9√5-15-(21+7√5-9√5-15)]/[3²-(√5)²]
= [21-7√5+9√5-15-21-7√5+9√5+15]/( 9-5)
= ( -14√5+18√5 )/4
= 4√5/4
= √5 ---( 1 )
= a + b√5 ---( 2 ) [ RHS ]
compare equation ( 1 ) and ( 2 ) , we get
a = 0 , b = 1
I hope this helps you.
: )
LHS = [ (7+3√5)/(3+√5)]-[(7-3√5)/(3-√5)]
=[(7+3√5)(3-√5)-(7-3√5)(3+√5)]/[(3+√5)(3-√5)]
= [21-7√5+9√5-15-(21+7√5-9√5-15)]/[3²-(√5)²]
= [21-7√5+9√5-15-21-7√5+9√5+15]/( 9-5)
= ( -14√5+18√5 )/4
= 4√5/4
= √5 ---( 1 )
= a + b√5 ---( 2 ) [ RHS ]
compare equation ( 1 ) and ( 2 ) , we get
a = 0 , b = 1
I hope this helps you.
: )
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Answer:Hi, please tell me if the answer is correct
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