Question

Ifa2+b2=29 and ab=10, find (i)a+b(ii)a–b​

Answer 1

Answer:

(i)7 or -7

(ii) 3 or -3

Step-by-step explanation:

(a+b)2=a2+b2+2ab

(a+b)2= 29+2*10

= 49

a+b = √49

= +7or -7

similarly,

(a-b)2=a2+b2-2ab

= 29-2*10

= 9

a-b = +3 or -3

Answer 2

Given:

• a² + b² = 29
• ab = 10

To find:

1. (a + b)
2. (a - b)

Method:

(a + b)² = a² + b² + 2ab

⇒(a + b)² = 29 + (2×10)

⇒(a + b)² = 29 + 20

⇒(a + b)² = 49

⇒(a + b) = √49

⇒(a + b) = 7

(a - b)² = a² + b² - 2ab

⇒(a - b)² = 29 - (2×10)

⇒(a - b)² = 29 - 20

⇒(a - b)² = 9

⇒(a - b)² = √9

⇒(a - b)² = 3