Question

If a and b are rational numbers, find a and b
√5-2/√5+2-√5+2/√5-2=a+b√5

Answer 1

Answer:

\frac{2-\sqrt{5}}{2+\sqrt{5}}\\\;\\\text{Multiplying Numerator and denominator by } 2-\sqrt{5}\\\;\\=\frac{(2-\sqrt{5})(2-\sqrt{5})}{(2+\sqrt{5})(2-\sqrt{5})}\\\;\\=\frac{(2\times2)-(2\times\sqrt{5})-(2\times\sqrt{5})+(\sqrt{5}\times\sqrt{5})}{(2^2-(\sqrt{5})^2)}\;\;\;\;\;\;\because(a+b)(a-b)=a^2-b^2\\\;\\=\frac{4-2\sqrt{5}-2\sqrt{5}+5}{4-5}\\\;\\=\frac{9-4\sqrt{5}}{-1}\\\;\\=4\sqrt{5}-9

Hence,

Answer 2

Answer:

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