Question

1. If a + b = 6 and ab = 5, calculate (i) a - b (ii) a2
+ b2
(iii) a2
- b2

Answer 1

Answer:

Given :

• a + b = 6
• a x b = 5

To find :

• a - b
• a² + b ²
• a² - b²

Solution :

• a + b = 6
• a = 6 - b
• Putting the valve of a
• a x b = 5
• (6 - b) x b = 5
• 6b - b² = 5
• 0 = b² - 6b + 5
• 0 = b² - b - 5b + 5
• 0 = b ( b - 1 ) - 5 ( b - 1 )
• 0 = ( b - 1 ) ( b - 5 )
• Either b - 1 = 0 or b - 5 = 0
• Either b = 1 or b = 5

Hence a = 1 or 5 and b = 1 or 5

• If a = 1 then b = 5
• If a = 5 then b = 1

i ) a - b

If a = 1 then b = 5 OR If a = 5 then b = 1

• 1 - 5 or 5 - 1
• (-4) or 4

ii) a² + b²

If a = 1 then b = 5 OR If a = 5 then b = 1

• 1² + 5² or 5² + 1²
• 1 + 25 or 25 + 1
• 26 or 26

iii) a² - b²

If a = 1 then b = 5 OR If a = 5 then b = 1

• 1² - 5² or 5² - 1²
• 1 - 25 or 25 - 1
• (-24) or 24