Study the given statements. Statement I: \[\frac{{{({{a}^{2}}-{{b}^{2}})}^{3}}+{{({{b}^{2}}-{{c}^{2}})}^{3}}+{{({{c}^{2}}-{{a}^{2}})}^{3}}}{{{(a+b)}^{3}}{{(b+c)}^{3}}+{{(c+a)}^{3}}}\] Statement II: \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca\] \[=\frac{1}{2}\left[ {{(a-b)}^{2}}+{{(b-c)}^{2}}+{{(c-a)}^{2}} \right]\] Which of the following options holds?

Both Statement-I and Statement-II are false.

Both Statement-I and Statement-II are true.

Statement-I is true but Statement-II is false.

Statement-I is false but Statement-II is true.

Study the given statements. Statement I: \[\frac{{{({{a}^{2}}-{{b}^{2}

1.	Study the given statements. Statement I: \[\frac{{{({{a}^{2}}-{{b}^{2}})}^{3}}+{{({{b}^{2}}-{{c}^{2}})}^{3}}+{{({{c}^{2}}-{{a}^{2}})}^{3}}}{{{(a+b)}^{3}}{{(b+c)}^{3}}+{{(c+a)}^{3}}}\] Statement II: \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca\] \[=\frac{1}{2}\left[ {{(a-b)}^{2}}+{{(b-c)}^{2}}+{{(c-a)}^{2}} \right]\] Which of the following options holds?
A.	Both Statement-I and Statement-II are true.
B.	Statement-I is true but Statement-II is false.
C.	Statement-I is false but Statement-II is true.
D.	Both Statement-I and Statement-II are false.
Answer» D. Both Statement-I and Statement-II are false.

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