If p+q=5,prove p3+q3+15pq=125
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Answer:
Using the identity (a+b)
3
=a
3
+b
3
+3ab(a+b), we can write
(p+q)
3
=p
3
+q
3
+3pq(p+q)
It is given that p+q=5 and pq=6, therefore,
(p+q)
3
=p
3
+q
3
+3pq(p+q)
⇒(5)
3
=p
3
+q
3
+(3×6)(5)
⇒125=p
3
+q
3
+(18×5)
⇒125=p
3
+q
3
+90
⇒p
3
+q
3
=125−90
⇒p
3
+q
3
=35
Hence, p
3
+q
3
=35.
Step-by-step explanation:
Hope it's useful
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