Question

If a and b are rational numbers such that
(2-√5) / (2 + √5) = a√5 + b​

Answer 1

Answer:

a=4 b=9

Step-by-step explanation:

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Answer 2

Answer:

a= -√5 and b=4

Step-by-step explanation:

$(2-\sqrt{5})(2+\sqrt{5})\\ It\ is\ in\ the\ form\ of\ (a+b)(a-b).\\As\ (a+b)(a-b)=a^2-b^2,\\So\ here:\\2^2-(\sqrt{5})^2=a\sqrt{5}+b\\4-5=a\sqrt{5}+b\\-5+4=a\sqrt{5}+b\\On\ comparing\ both\ the\ sides,\\a\sqrt{5}=-5\ and\ b=4\\ or\ a=-\sqrt{5}\ and\ b=4$