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If p³ - q³ = (p - q){(p + q)² - xpq}, then the value of x is?

11
2-1
32
4-2

Answer:- 1

Explanation:-

Solution:

\begin{aligned} p^{3} - q^{3} = (p - q) {p^{2} + q^{2} + p q} \\ \Rightarrow (p - q) {{(p + q)}^{2} - x p q} = (p - q) (p^{2} + q^{2} + p q) \\ \Rightarrow p^{2} + q^{2} + 2 p q - x p q = p^{2} + q^{2} + p q \\ \Rightarrow 2 p q - p q = x p q \\ \Rightarrow p q = x p q \\ \Rightarrow x = 1 \end{aligned}

$\eqalign{ & {p^3} - {q^3} = \left( {p - q} \right)\left\{ {{p^2} + {q^2} + pq} \right\} \cr & \Rightarrow \left( {p - q} \right)\left\{ {{{\left( {p + q} \right)}^2} - xpq} \right\} = \left( {p - q} \right)\left( {{p^2} + {q^2} + pq} \right) \cr & \Rightarrow {p^2} + {q^2} + 2pq - xpq = {p^2} + {q^2} + pq \cr & \Rightarrow 2pq - pq = xpq \cr & \Rightarrow pq = xpq \cr & \Rightarrow x = 1 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} p^{3} - q^{3} = (p - q) {p^{2} + q^{2} + p q} \\ \Rightarrow (p - q) {{(p + q)}^{2} - x p q} = (p - q) (p^{2} + q^{2} + p q) \\ \Rightarrow p^{2} + q^{2} + 2 p q - x p q = p^{2} + q^{2} + p q \\ \Rightarrow 2 p q - p q = x p q \\ \Rightarrow p q = x p q \\ \Rightarrow x = 1 \end{aligned}

$\eqalign{ & {p^3} - {q^3} = \left( {p - q} \right)\left\{ {{p^2} + {q^2} + pq} \right\} \cr & \Rightarrow \left( {p - q} \right)\left\{ {{{\left( {p + q} \right)}^2} - xpq} \right\} = \left( {p - q} \right)\left( {{p^2} + {q^2} + pq} \right) \cr & \Rightarrow {p^2} + {q^2} + 2pq - xpq = {p^2} + {q^2} + pq \cr & \Rightarrow 2pq - pq = xpq \cr & \Rightarrow pq = xpq \cr & \Rightarrow x = 1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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