If aover b+bover a = 1, a ≠ 0, b ≠ 0, then find the value of a³+b³over 3ab .

If aover b+bover a = 1, a ≠ 0, b ≠ 0, then find the value…

If ${a\over b}+{b\over a}$ = 1, a ≠ 0, b ≠ 0, then find the value of ${a^3+b^3}\over 3ab$ .

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 0.

${a\over b}+{b\over a}$ = 1

⇒ $\frac{a^2 + b^2}{ab}$ = 1

⇒ $a^2 + b^2 = ab$

⇒ $a^3 +b^3 = (a+b)(a^2+b^2-ab)$ ......(i)

substituting value of $a^2+b^2$ in equation (i)

⇒ $a^3+b^3 = 0$

ATQ

⇒ ${a^3+b^3}\over 3ab$