Question

If x is real, then greatest and least values of x2−x+1x2+x+1x2−x+1x2+x+1 are

Answer 1

Answer:

If x is real, then the greatest and the least values of (x2 - x + 1)/(x2 + x + 1) are (A) 3, -1/2 (B) 3, 1/3 (C) -3, -1/3 (D) None of these Read more on Sarthaks.com - https://www.sarthaks.com/556970/if-x-is-real-then-the-greatest-and-the-least-values-of-x-2-x-1-x-2-x-1-are

Answer 2

Answer:

greatest value = (13+6√2)/7

least value = (11-6√2)/7

Step-by-step explanation:

let, f(x) = (x²-x+1)/(x²+x+1)

Differentiating with respect to X,

f'(x)

= {(x²+x+1)(2x-1)-(x²-x+1)(2x+1)}/(x²+x+1)²

f'(x)=0 for maximum and minimum

{(x²+x+1)(2x-1)-(x²-x+1)(2x+1)}/(x²+x+1)² = 0

or,

(x²+x+1)(2x-1)-(x²-x+1)(2x+1) = 0

or

(x²+x+1)(2x-1) = (x²-x+1)(2x+1)

or,

2x³+x²+x-1 = 2x³-x²+x+1

or,

x²=2 , x = √2, -√2

Now,

putting x value in f(x)

f(√2) = (11-6√2)/7 and

f(-√2) = (13+6√2)/7

so,

greatest value = (13+6√2)/7

least value = (11-6√2)/7