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प्रश्न
Simplify.
(7a − 6b + 5c)2 + (7a + 6b − 5c)2
उत्तर
It is known that,
\[\left( a + b + c \right)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\]
\[\ \left( 7a - 6b + 5c \right)^2 + \left( 7a + 6b - 5c \right)^2 \]
\[ = \left( 7a \right)^2 + \left( - 6b \right)^2 + \left( 5c \right)^2 + 2 \times 7a \times \left( - 6b \right) + 2 \times \left( - 6b \right) \times 5c + 2 \times 5c \times 7a + \left( 7a \right)^2 + \left( 6b \right)^2 + \left( - 5c \right)^2 + 2 \times 7a \times 6b + 2 \times 6b \times \left( - 5c \right) + 2 \times \left( - 5c \right) \times 7a\]
\[ = 49 a^2 + 36 b^2 + 25 c^2 - 84ab - 60bc + 70ca + 49 a^2 + 36 b^2 + 25 c^2 + 84ab - 60bc - 70ca\]
\[ = 98 a^2 + 72 b^2 + 50 c^2 - 120bc\]
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