if a²+b²=13 and ab=6, find : 1. a+b 2. a-b
Answers
Answered by
3
Answer:
3(a+b)
2
−2(a−b)
2
We know,
(a+b)
2
=a
2
+b
2
+2ab
=13+2(6)
=13+12
=25
=>(a+b)=±
25
=>(a+b)=±5
Again,
(a−b)
2
=a
2
+b
2
−2ab
=13−2(6)
=13−12
=1
=>(a−b)=±1
Putting the values, we get,
3(±5)
2
−2(±1)
2
=75−2
=73
Answered by
23
Step-by-step explanation:
Given:
a² + b² = 13
ab = 6
To find:
1. a + b
2. a - b
Solution:
We know,
- (a + b)² = a² + b² + 2ab
⇒ (a + b)² = 13 + 2(6)
⇒ (a + b)² = 13 + 12
⇒ (a + b)² = 25
Square root on both sides.
- √(a + b)² = √25
∴ (a + b) = ±5
We know,
- (a - b)² = a² + b² - 2ab
⇒ (a - b)² = 13 - 2(6)
⇒ (a - b)² = 13 - 12
⇒ (a - b)² = 1
Square root on both sides.
- √(a - b)² = √1
∴ (a - b) = ±1
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