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Question Number 9548 by Joel575 last updated on 14/Dec/16

a - 7 b + 8 c = 4

8 a + 4 b - c = 7

a, b, c \in R

60 (a^{2} - b^{2} + c^{2}) = ?

Answered by ridwan balatif last updated on 15/Dec/16

a - 7 b + 8 c = 4

a + 8 c = 4 + 7 b

{(a + 8 c)}^{2} = {(4 + 7 b)}^{2}

a^{2} + 16 ac + {64 c}^{2} = 16 + 56 b + {49 b}^{2} \dots (1)

8 a + 4 b - c = 7

8 a - c = 7 - 4 b

{(8 a - c)}^{2} = {(7 - 4 b)}^{2}

{64 a}^{2} - 16 ac + c^{2} = 49 - 56 b + {16 b}^{2} \dots (2)

(1) + (2)

a^{2} + 16 ac + {64 c}^{2} = 16 + 56 b + {49 b}^{2}

{64 a}^{2} - 16 ac + c^{2} = 49 - 56 b + {16 b}^{2}

- - - - - - - - - - - - - - - - - - +

{65 a}^{2} + {65 c}^{2} = 65 + {65 b}^{2}

a^{2} + c^{2} = 1 + b^{2}

a^{2} - b^{2} + c^{2} = 1

60 (a^{2} - b^{2} + c^{2}) = 60

Commented by Joel575 last updated on 23/Dec/16

m a k a s i h k k

t e r b a i k

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