First slide

Theory of expressions

Question

If x be real, then the minimum value of $x^{2} - 8 x + 17$ is

Moderate

A

$- 1$
B

$0$
C

$1$
D

$2$

Solution

$x^{2} - 8 x + 17 = (x^{2} - 8 x + 16) + 1 = {(x - 4)}^{2} + 1$
Since x is real, so ${(x - 4)}^{2}$ is always positive and its least value is 0 and so the minimum value of given expression is 1.

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