Question

find the sum :
(I) l²+m²,m²+n²,n²+l²
(II) 3p²q²-2pq+5,8pq-5p²q²​

Answer 1

Answer:

$1) \: ({l}^{2} + {m}^{2} ) + ( {m}^{2} + {n}^{2} ) + ( {n}^{2} + {l}^{2} ) \\ \\ = {l}^{2} + {m}^{2} + {m}^{2} + {n}^{2} + {n}^{2} + {l}^{2} \\ \\ = {l}^{2} + {l}^{2} + 2 {m}^{2} + 2 {n}^{2} \\ \\ = 2 {l}^{2} + 2 {m}^{2} + 2 {n}^{2} \\ \\ = 2( {l}^{2} + {m}^{2} + {n}^{2} ) \\ \\ 2) \: (3 {p}^{2} {q}^{2} - 2pq + 5) + (8pq - 5 {p}^{2} {q}^{2} ) \\ \\ = 3 {p}^{2} {q}^{2} - 2pq + 5 + 8pq - 5 {p}^{2} {q}^{2} \\ \\ = 3 {p}^{2} {q}^{2} - 5 {p}^{2} {q}^{2} - 2pq + 8pq + 5 \\ \\ = - 2 {p}^{2} {q}^{2} + 6pq + 5$

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