If `a+b=10\ \ a n d\ \ \ a b=16` , find the value of `a^2-a b+b^2\ a n d\ \ a^2+a b+b^2`

Explanation

Given :` a + b = 10 ............(1)`
and `ab = 16 .....................(2)`
It is known that,
`(a + b)^2= a^2 + 2ab + b^2 `
Now, substituting the values of` (1)` and `(2)` in the above, we get.
`⇒ (10)^2 = a^2 + 2 xx (16) + b^2`
`⇒ 100 = a^2 + 32 + b^2`
`⇒ a^2 + b^2 = 100 - 32`
`⇒ a^2 + b^2 = 68 .................(3)`
Now, substituting the value of `a^2 + b^2 = 68` in `a^2 + b^2- ab `
`=68 - 16 (`as `ab = 16)`
`=52`
And, substituting the value of `a^2 + b^2 = 68` in `a^2 + ab + b^2 `
`= 68 + 16= 84`