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If a=7, b=5 and =3, the value of \( \Large a^{2}+b^{2}+c^{2}-ab-bc-ca \) is
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A) 12 |
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B) -12 |
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C) 0 |
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D) 18 |
Correct Answer:
| A) 12 |
Description for Correct answer:
\( \Large a^{2}+b^{2}+c^{2}-ab-bc-ca \)
=\( \Large \frac{1}{2}\left[ \left(a-b\right)^{2}+ \left(b-c\right)^{2}+ \left(c-a\right)^{2} \right] \)
= \( \Large \frac{1}{2}\left[ \left(7-5\right)^{2}+ \left(5-3\right)^{2}+ \left(3-7\right)^{2} \right] \)
= \( \Large \frac{1}{2} \left(4+4+16\right)=\frac{24}{2}=12 \)
\( \Large a^{2}+b^{2}+c^{2}-ab-bc-ca \)
=\( \Large \frac{1}{2}\left[ \left(a-b\right)^{2}+ \left(b-c\right)^{2}+ \left(c-a\right)^{2} \right] \)
= \( \Large \frac{1}{2}\left[ \left(7-5\right)^{2}+ \left(5-3\right)^{2}+ \left(3-7\right)^{2} \right] \)
= \( \Large \frac{1}{2} \left(4+4+16\right)=\frac{24}{2}=12 \)
Part of solved Elementary Mathematics questions and answers : >> Elementary Mathematics
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