Question

if a+b=10 and ab=16, find the value of a2-ab+b2 and a2+ab+b2 .

Answer 1

Solution :-

Given : a + b = 10 ............(1)
and ab = 16 .....................(2)

It is known that,

(a + b)² = a² + 2ab + b² 

Now, substituting the values of (1) and (2) in the above, we get.

⇒ (10)² = a² + 2*(16) + b²

⇒ 100 = a² + 32 + b²

⇒ a² + b² = 100 - 32

⇒ a² + b² = 68 .................(3)

Now, substituting the value of a² + b² = 68 in a² - ab + b²

⇒ 68 - 16 (as ab = 16)

⇒ 52

And, substituting the value of a² + b² = 68 in a² + ab + b² 

⇒ 68 + 16

⇒ 84

Answer.

Answer 2

a square+ab+b square

use identity

(a+b)square =a square+2×16+b square

(10) square =a square +32+b square

100-32=a square+b square

68=a square +b square

a square-ab+b square

use identity

(a-b)square =a square-16+b square

(a-b)square =a square +b square-16

(a-b)square =68-16

(a-b)square =52

a square+ab+b square

68+16

84 answer