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a-7b-8c-4-8a-4b-c-7-a-b-c-R-60-a-2-b-2-c-2-

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Question Number 9548 by Joel575 last updated on 14/Dec/16
a − 7b + 8c = 4 8a + 4b − c = 7 a, b, c ∈ R 60(a^2 − b^2 + c^2 ) = ?
a−7b+8c=48a+4b−c=7a,b,c∈R60(a2−b2+c2)=?
Answered by ridwan balatif last updated on 15/Dec/16
a−7b+8c=4 a+8c=4+7b (a+8c)^2 =(4+7b)^2 a^2 +16ac+64c^2 =16+56b+49b^2 ...(1) 8a+4b−c=7 8a−c=7−4b (8a−c)^2 =(7−4b)^2 64a^2 −16ac+c^2 =49−56b+16b^2 ...(2) (1)+(2) a^2 +16ac+64c^2 =16+56b+49b^2 64a^2 −16ac+c^2 =49−56b+16b^2 −−−−−−−−−−−−−−−−−−+ 65a^2 +65c^2 =65+65b^2 a^2 +c^2 =1+b^2 a^2 −b^2 +c^2 =1 60(a^2 −b^2 +c^2 )=60
a−7b+8c=4a+8c=4+7b(a+8c)2=(4+7b)2a2+16ac+64c2=16+56b+49b2…(1)8a+4b−c=78a−c=7−4b(8a−c)2=(7−4b)264a2−16ac+c2=49−56b+16b2…(2)(1)+(2)a2+16ac+64c2=16+56b+49b264a2−16ac+c2=49−56b+16b2−−−−−−−−−−−−−−−−−−+65a2+65c2=65+65b2a2+c2=1+b2a2−b2+c2=160(a2−b2+c2)=60
Commented by Joel575 last updated on 23/Dec/16
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