f-x-x-2-6x-10-f-3-2-6-

Question Number 217842 by aylinrabbani last updated on 22/Mar/25

f (x) = \sqrt{x^{2} - 6 x + 10}

f (3 + 2 \sqrt{6}) = ?

Answered by Rasheed.Sindhi last updated on 22/Mar/25

f (x) = \sqrt{x^{2} - 6 x + 10}

= \sqrt{x^{2} - 6 x + 9 + 1}

= \sqrt{{(x - 3)}^{2} + 1}

f (3 + 2 \sqrt{6}) = \sqrt{{(3 + 2 \sqrt{6} - 3)}^{2} + 1}

= \sqrt{{(2 \sqrt{6})}^{2} + 1}

= \sqrt{4 (6) + 1}

= \sqrt{25}

= 5

Answered by AntonCWX8 last updated on 22/Mar/25

{(3 + 2 \sqrt{6})}^{2} - 6 (3 + 2 \sqrt{6}) + 10

= 9 + 12 \sqrt{6} + 24 - 18 - 12 \sqrt{6} + 10

= 25

\sqrt{25} = \pm 5

Commented by mr W last updated on 22/Mar/25

\sqrt{25} = 5 \neq \pm 5

Commented by Frix last updated on 22/Mar/25

If \sqrt{25} = \pm 5 then \sqrt{25} + \sqrt{25} = ?

(a) - 10

(b) 0

(c) 10

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