Question

if a + b = 10 and ab = 16 find the value of a^2 - ab + b^2 and a^2 + ab + b^2

Answer 1

Answer:

Step-by-step explanation:

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 2

(a + b)3 = a3 + b3 + 3ab(a +b)

(10)3 = a3 + b3 + 3*16(10)

1000 = a3 + b3 + 480

a3 + b3 = 1000 -480 = 520

a3 +b3 = ( a+ b) (a2 - ab + b2)

520 = 10(a2 - ab +b2)

a2 - ab + b2 = 520 / 10 = 52

if we see 8 + 2 = 10 , 8 * 2 = 16

a - b = 8 - 2 = 6

(8)2 + (2)2 + 16
= 64 + 16 + 4 = 64 +20
= 84
= a2 + ab + b2