Find the value of p^2 + q^2 if p -q=6 and p+q=14
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Answered by
191
square both equations and add them
(p-q)² = p²+q²-2pq
(p+q)²= p²+ q²+ 2pq
(p-q)² + (p+q)² = 2(p²+q²)
6²+14² = 2(p²+q²)
p²+q² = 232/2 = 116
(p-q)² = p²+q²-2pq
(p+q)²= p²+ q²+ 2pq
(p-q)² + (p+q)² = 2(p²+q²)
6²+14² = 2(p²+q²)
p²+q² = 232/2 = 116
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Answered by
53
Answer:
Value of p²+q² = 116
Explanation:
Given p-q=6 ----(1)
p+q=14 ----(2)
Add equations (1) and (2) ,we get
=> p-q+p+q=6+10
=> 2p = 20
=> p = 20/2
=> p = 10
Substitute p=10 in equation (2), we get
=> 10+q = 14
=> q = 14-10
=> q = 4
Now ,
Value of p²+q²
= 10²+4²
= 100+16
= 116
Therefore,
p²+q² = 116
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