Question

If a+b=11 and ab=28, find a-b using appropriate identities

Answer 1

a+b = 11

Square the equation,

(a+b)^2 = (11)^2 = 121

=> a^2 + b^2 +2ab = 121

=> a^2 + b^2 = 121 - 2ab

= 121 - 56

=> a^2 + b^2 = 65 .................(a)

and,

ab = 28

Multiply the equation by 2,

2ab = 2(28) = 56 ......................(b)

Also,

(a-b)^2 = a^2 + b^2 - 2ab

= 65 - 56.....................(from (a) and (b))

(a-b)^2 = 9

Square root the above equation,

=> a - b = 3

Hence, the required value of (a-b) is 3.

Answer 2

Answer :-

(a + b) ² = a² + b² + 2ab

(11)² = a² + b² + 2(28) {ab = 28, a + b = 11}

121 - 56 = a² + b²

a² + b² = 65

(a - b) ² = a² + b² - 2ab

(a - b)² = 65 - 2(28) {a² + b² = 65, ab = 28}

(a - b)² = 65 - 56

(a - b)² = 9

(a - b) = 3

Hence, (a - b) = 3