If p + q = 8 and pq = 6 , find the value of p^2+q^2 .
Answers
Answered by
2
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.
Answered by
1
Answer:
Given,
p + q = 8 & pq = 6 ; p^2 + q^2 = ?
A.T.Q,
(p + q) = 8
squaring both side
(p + q)^ 2 = (8)^2
or, p^2 + 2pq + q^2 = 64
or, p^2 + 2×6 + q^2 = 64
or, p^2 + 12 + q^2 = 64
or, p^2 + q^2 = 64 - 12
or, p^2 + q^2 = 52 (ans.)
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