Question

If 2+√5/2−√5=a + b√5, then a =

Answer 1

Step-by-step explanation:

a²-b²

=[2-√5/2+√5]²-[2+√5/2-√5]²

=[2-√5]²/[2+√5]²-[2+√5]²/[2-√5]²

=[4+5-4√5/4+5+4√5]-[4+5+4√5/4+5-4√5]²

=[9-4√5/9+4√5]-[9+4√5/9-4√5]

=[9-4√5]²-[9+4√5]²/9²-[4√5]²

=81+80-72√5-81-80-72√5/81-80

=-144√5/1

=-144√5

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Answer 2

Step-by-step explanation:

2+✓5/2-√5=a+b√5

2+√5-2√5/2=a+b√5

2+(-√5/2)=a+b√5

2-√5/2=a+b√5

by comparing

a=2,. b=-1/2

therefore a=2

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