Question

If a² + b² = 29 and ab = 10; find: (i) a+b

(ii) a-b​

Answer 1

a + b = 7

a - b = 3

Given :-

• a² + b² = 29

• ab = 10

Formulas used :-

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

Answer :-

( a + b )² = a² + b² + 2ab

= 29 + (2× 10)

= 29 + 20

= 49

• a + b = √49
• a + b = 7 -------------(1)

$\rule{15cm}{0.02cm}$

(a - b)² = a² + b² - 2ab

= 29 - (2×10)

= 29 - 20

= 9

• a - b = √9
• a - b = 3 --------------(2)

$\rule{15cm}{0.02cm}$

a + b = 7

a - b = 3