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If a(a + b + c) = 45, b(a + b + c) = 75 and c(a + b + c) = 105, then what is the value of (a2 + b2 + c2)?
- A75
- B83
- C217
- D225
Answer not set
Discussion 1
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CCommunity
Given: a2 + ab + ac = 45 .…(i)
b(a + b + c) = 75 .…(ii)
c(a + b + c) = 105 .…(iii)
by (i), (ii) and (iii)
45/a = 75/b = 105/c
⇒ 3/a = 5/b = 7/c
So, a = 3, b = 5, c = 7
∴ a2 + b2 + c2 = 32 + 52 + 72 = 83
b(a + b + c) = 75 .…(ii)
c(a + b + c) = 105 .…(iii)
by (i), (ii) and (iii)
45/a = 75/b = 105/c
⇒ 3/a = 5/b = 7/c
So, a = 3, b = 5, c = 7
∴ a2 + b2 + c2 = 32 + 52 + 72 = 83