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Question Number 47531 by peter frank last updated on 11/Nov/18

Commented by math1967 last updated on 11/Nov/18

question should be A±(√((A+G)(A−G)))

questionshouldbeA±(A+G)(A−G)

Commented by peter frank last updated on 11/Nov/18

yes sir.thanks for correction

yessir.thanksforcorrection

Answered by math1967 last updated on 11/Nov/18

let two numbers are a,b ∴A=((a+b)/2) ,G=(√(ab)) ∴a+b=2A again (a−b)^2 =(a+b)^2 −4ab ⇒(a−b)^2 =4A^2 −4G ∴a−b=±2(√(A^2 −G^2 )) a+b=2A by solving two numbers are A+(√(A^2 −G^2 )) and A−(√(A^2 −G^2 )) or A±(√((A+G)(A−G)))

lettwonumbersarea,b∴A=a+b2,G=ab∴a+b=2Aagain(a−b)2=(a+b)2−4ab⇒(a−b)2=4A2−4G∴a−b=±2A2−G2a+b=2AbysolvingtwonumbersareA+A2−G2andA−A2−G2orA±(A+G)(A−G)

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