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

11
2-1
33
42

Answer:- 1

Explanation:-

Solution:

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

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

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

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

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