Question

If a=2-root5/2+root5 and b=2+root5/2-root5 , find a2 -b2

Answer 1

a=(2-√5)/(2+√5)
={(2-√5)(2-√5)}/{(2+√5)(2-√5)}
=(2-√5)²/(2²-√5²)
=(4-4√5+5)/(4-5)
=(9-4√5)/(-1)
=-(9-4√5)
∴, a²={-(9-4√5)}²=81-72√5+80=161-72√5
b=(2+√5)/(2-√5)
=(2+√5)(2+√5)/(2-√5)(2+√5)
=(2+√5)²/(2²-√5²)
=(4+4√5+5)/(4-5)
=(9+4√5)/(-1)
=-(9+4√5)
∴, b²={-(9+4√5)}²=81+72√5+80=161+72√5
∴, a²-b²=161-72√5-161-72√5=-144√5

Answer 2

Answer:

HII ! IN THE ABOVE IMAGE IS THE ANSWER

Step-by-step explanation:

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