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Question Number 90581 by hardylanes last updated on 24/Apr/20

given that α and β are roots of  the equation   aχ^2 +bχ+c=0. show that λμb^2 =ac(λ+μ)^(2 )   where (α/β)=(λ/μ)

giventhatαandβarerootsoftheequationaχ2+bχ+c=0.showthatλμb2=ac(λ+μ)2whereαβ=λμ

Answered by maths mind last updated on 24/Apr/20

⇔λμ(b^2 /a^2 )=(c/a)(λ+μ)^2 ⇔(λ/μ).(b^2 /a^2 )=(c/a)((λ/μ)+1)^2 ..E  ((b/a))^2 =(α+β)^2   (c/a)=αβ  E⇔(α/β)(α+β)^2 =αβ(1+(α/β))^2 =(α/β)(α+β)^2 ..True

λμb2a2=ca(λ+μ)2λμ.b2a2=ca(λμ+1)2..E(ba)2=(α+β)2ca=αβEαβ(α+β)2=αβ(1+αβ)2=αβ(α+β)2..True

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