Question

Find the value of a in 3 - square root 5 / 3 + 2 square root 5 = a square root 5 - 19/11

Answer 1

=(3-√5)/(3+2√5)

multiply with conjugate

=(3-√5)/(3+2√5)×(3-2√5)/(3-2√5)

=(3-√5)(3-2√5)/(3+2√5)(3-2√5)

=[3(3-2√5)-√5(3-2√5)]/(3²-(2√5)²

=(3²-6√5-3√5+2(5))/(9-4(5))

=(9-9√5+10)/(9-20)

=(19-9√5)/(-11)

=–(19-9√5)/ 11

= –(19-9√5)/11

=(-19+9√5)/11

=(9√5-19)/11

=9√5/11 - 19/11 = a√5-19/11

Therefore,a=9/11

If the question was root (a√5-19)/11 then a=9

But according to the question, root(a√5-19)/11

So, the answer is 9/11