a-b-c-Z-and-a-2-b-2-c-2-ab-bc-ca-2025-find-out-all-triplets-a-b-c-

Question Number 217958 by dscm last updated on 23/Mar/25

a, b, c \in Z^{+} a n d

a^{2} + b^{2} + c^{2} + a b + b c + c a = 2025

f i n d o u t a l l t r i p l e t s (a, b, c) .

Commented by Unhombre last updated on 24/Mar/25

y o u c a n a l s o u s e t h i s ↓

a^{2} + b^{2} + c^{2} + 2 a b + 2 a c + 2 b c =

{(a + b + c)}^{2}

Commented by Frix last updated on 24/Mar/25

{(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + a c + b c)

Answered by mehdee7396 last updated on 24/Mar/25

a + b = x & a + c = y & b + c = z

\Rightarrow x^{2} + y^{2} + z^{2} = 4050

\Rightarrow x = 40 & y = 35 & z = 35

\Rightarrow a = b = 20 & c = 15

Answered by mahdipoor last updated on 23/Mar/25

{(a + b)}^{2} + {(b + c)}^{2} + {(c + a)}^{2} =

2 (a^{2} + b^{2} + c^{2} + a b + b c + c a) = 2 \times 2025

\Rightarrow 4050 = x^{2} + y^{2} + z^{2}

\Rightarrow x, y, z = \dots

\Rightarrow a, b, c = \dots