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Question Number 29723 by ajfour last updated on 11/Feb/18

Commented by ajfour last updated on 11/Feb/18

Express c in terms of a, b .

Expresscintermsofa,b.

Answered by mrW2 last updated on 11/Feb/18

Commented by ajfour last updated on 12/Feb/18

Thank you Sir.

ThankyouSir.

Commented by mrW2 last updated on 11/Feb/18

cos α=(b/a) β=π−α CB=(√(a^2 −b^2 )) BD=b−(√(a^2 −b^2 )) c^2 =a^2 +(b−(√(a^2 −b^2 )))^2 −2a(b−(√(a^2 −b^2 )))cos β c^2 =a^2 +(b−(√(a^2 −b^2 )))^2 +2a(b−(√(a^2 −b^2 )))cos α c^2 =a^2 +(b−(√(a^2 −b^2 )))^2 +2a(b−(√(a^2 −b^2 )))(b/a) c^2 =a^2 +(b−(√(a^2 −b^2 )))^2 +2b(b−(√(a^2 −b^2 ))) c^2 =a^2 +b^2 +a^2 −b^2 −2b(√(a^2 −b^2 ))+2b^2 −2b(√(a^2 −b^2 )) c^2 =2(a^2 +b^2 −2b(√(a^2 −b^2 ))) ⇒c=(√(2(a^2 +b^2 −2b(√(a^2 −b^2 )))))

cosα=baβ=π−αCB=a2−b2BD=b−a2−b2c2=a2+(b−a2−b2)2−2a(b−a2−b2)cosβc2=a2+(b−a2−b2)2+2a(b−a2−b2)cosαc2=a2+(b−a2−b2)2+2a(b−a2−b2)bac2=a2+(b−a2−b2)2+2b(b−a2−b2)c2=a2+b2+a2−b2−2ba2−b2+2b2−2ba2−b2c2=2(a2+b2−2ba2−b2)⇒c=2(a2+b2−2ba2−b2)

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