Question : If $p^{3}-q^{3}=(p-q)[(p+q)^{2}-xpq$, then the value of $x$ is:
Option 1: 1
Option 2: –1
Option 3: 2
Option 4: –2
Answer (1)
25th Jan, 2024
Correct Answer: 1
Solution :
Given: $p^{3}-q^{3}=(p-q)[(p+q)^{2}–xpq]$
⇒ $p^{3}-q^{3}=(p-q)(p^{2}+q^{2}+2pq–xpq)$
⇒ $p^{3}-q^{3}=(p-q)(p^{2}+q^{2}+pq(2-x)$ ----(1)
We know the formula of $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$
Comparing this with equation (1), we have:
⇒ $(2-x)=1$
⇒ $x=1$
Hence, the correct answer is 1.
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