If a b-b a-1- then a3-b3-a 1b -1c 12d 0

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Expansion of (x^2 - y^2)

If a b+b a=1,...

Question

If $\frac{a}{b} + \frac{b}{a} = 1$ , then a³ + b³ =

(a) 1

(b) −1

(c) $\frac{1}{2}$

(d) 0

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Solution

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\frac{a}{b} + \frac{b}{a} = - 1

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∣ ∣ ∣ ∣ \begin{matrix} a & a + 1 & a - 1 - b & b + 1 & b - 1 c & c - 1 & c + 1 \end{matrix} ∣ ∣ ∣ ∣ + ∣ ∣ ∣ ∣ ∣ \begin{matrix} a + 1 & b + 1 & c - 1 a - 1 & b - 1 & c + 1 (- 1)^{n + 2} a & (- 1)^{n + 1} b & (- 1)^{n} c \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0

n

If $c o s e c θ - s i n θ = a^{3}$ and $s e c θ - c o s θ = b^{3}$ , then $a^{2} b^{2} (a^{2} + b^{2}) =$

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