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1. i.) (x+y) = x² + y² + 2xy
= 5 = x² + y² + 2(6)
= 5 = x² + y² +12
5 - 12 = x² + y²
So, x² + y² = -7
ii.) (x-y) = x² + y² - 2xy
6 = x² + y² - 2(16)
6 = x² + y² - 32
6 + 32 = x² + y²
So, x² + y² = 38
2. i.) (p+q) = p² + q² + 2pq
= 29 + 2(10)
= 29 + 20 = 39.
ii.) (p-q) = p² + q² - 2pq
= 29 - 2(10)
= 29 - 20 = 19.
3. i.) x + 1/x = 3
Squaring both sides:
(x + 1/x)² = 3²
x² + 1/x² + 2 = 9
x² + 1/x² = 9 - 2
x² + 1/x² = 7
ii.) x - 1/x = 4
Squaring both sides:
(x - 1/x)² = 4²
x² + 1/x² - 2 = 16
x² + 1/x² = 16 + 2
x² + 1/x² = 18
Step-by-step explanation:
Hope it helps :)
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