عدد حقيقي موجب تماماً، حل في IR2 جملة المعادلتين: x.y =a2 (Ln x)2 + (Ln y)2 = 5/2 (Ln a)2

x.y = a2

Ln x.y = Ln a2

Ln x + Ln y = 2 Ln a

Ln x = t

Ln y = h

Ln a = A

t+h = 2A          (1)

t2 + h2 = 5/2 * (Ln a)2 = 5/2 (Ln a)2

t2 + h2 = 5/2 A2          (2)

h = 2A-t

t2 + (2A-t)2 = 5/2 A2

t2 + 4A2 – 4At + t2 = 5/2 A2

4t2 – 8At + 3A2 = 0

∆ = 64 A2 – 48 A2 = 16 A2

√∆ = 4A

t = (+8A+4A)/8 = 3A/2

t = (+8A-4A)/8 = A/2

t = Ln x = 3A/2

Ln x = 3/2 Ln a

Ln x = Ln a^(3/2)

X = a^(3/2)

X = a√a

H = 2A – t = 2A – Ln x

h = Ln y = 2 Ln a – Ln a√a

Ln y = Ln (a2/a√a) = Ln √a

y = √a

ونجد ان حل المعادلتين (a√a,√a).