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1.
- A. 160
- B. 160
- C. 160
- D. 160
Answer: Option D
Explanation:
Given: a + b + c = 21 ab + bc + ca = 143
We want to find: a^2 + b^2 + c^2
Now, let's use the following identity: (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + ac + bc)
We know that (a + b + c)^2 = 21^2 = 441 and ab + bc + ca = 143.
Now, plug these values into the identity: 441 = a^2 + b^2 + c^2 + 2(143)
Simplify the equation: 441 = a^2 + b^2 + c^2 + 286
Now, isolate a^2 + b^2 + c^2: a^2 + b^2 + c^2 = 441 - 286 = 155
So, we have a^2 + b^2 + c^2 = 155.
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