Find the values of a and b if (3-√5)÷(3+2√5)=a√5-b
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(3-sqrt5)=(a*sqrt5-b)(3+2sqrt5)
3-sqrt5=3*sqrt5*a+2sqrt5*a-3b-2sqrt5*b
so (sqrt5*a-b)*3=3
sqrt5*a=b.........................1
-sqrt5=2sqrt5(a+b)
2a+2b=-1.........................2
2a+2*sqrt5*a=-1
so
a=-1/[2+2*sqrt5]
b=-sqrt5/[2+2*sqrt5]
3-sqrt5=3*sqrt5*a+2sqrt5*a-3b-2sqrt5*b
so (sqrt5*a-b)*3=3
sqrt5*a=b.........................1
-sqrt5=2sqrt5(a+b)
2a+2b=-1.........................2
2a+2*sqrt5*a=-1
so
a=-1/[2+2*sqrt5]
b=-sqrt5/[2+2*sqrt5]
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