If a + b = 7 and ab = 10: find a - b.
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Answered by
0
Answer:
a - b = ±3
Step-by-step explanation:
a + b =7 (i)
ab = 10 (ii)
from eq (i),
a = 7 - b (iii)
using (ii) and (iii),
ab = 10
(7 - b)b = 10
7b - b² - 10 = 0
b² - 7b + 10 = 0
b² - 5b - 2b + 10 = 0
b(b - 5) - 2(b - 5) = 0
(b - 5)(b - 2) = 0
b- 5 = 0 b - 2 = 0
b = 5 b = 2
a = 7 - b a = 7 - b
a = 7 - 5 a = 7 - 2
a = 2 a = 5
a - b a - b
5 - 2 2 - 5
3 -3
Answered by
0
ANSWER = ±3
a + b = 7
ab = 10
(a+b)² = a² + b² + 2ab
7² = a²+ b² + 2 ×10
a² + b² = 49 - 20
= 29
(a-b)² = a² + b² - 2ab
= 29 - 20
= 9
(a-b) =√9
(a-b) = ± 3
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