Surds identity and algebraic identity statements

Question

Given below are two statements:

Statement I: $\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}} + \frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}} = 2$

Statement II: If $a + b + c = 0$ , then $(a^3 + b^3 + c^3) \div abc = 3$

In light of the above statements, choose the correct answer from the options given below

Accepted Answer

D. Statement I: $$\frac{(\sqrt{7}+\sqrt{5})^2 + (\sqrt{7}-\sqrt{5})^2}{7-5} = \frac{2(7 + 5)}{2} = 12 
eq 2$$ So Statement I is false. Statement II: If $a + b + c = 0$, by algebraic identity $a^3 + b^3 + c^3 = 3abc$. Thus, $(a^3 + b^3 + c^3) \div abc = 3$. Statement II is true.

Answer

Both Statement I and Statement II are true

Answer

Both Statement I and Statement II are false

Answer

Statement I is true but Statement II is false

Answer

Statement I is false but Statement II is true

Surds identity and algebraic identity statements

Explanation

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