The-maximum-value-of-y-x-3-2-x-2-2-2-x-2-x-2-1-2-is-A-10-C-4-B-2-5-D-10-

Question Number 143997 by liberty last updated on 20/Jun/21

T h e m a x i m u m v a l u e o f

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

i s (A) \sqrt{10} (C) 4

(B) 2 \sqrt{5} (D) 10

Answered by mitica last updated on 20/Jun/21

(A) \sqrt{10}

Answered by mitica last updated on 20/Jun/21

A (x, x^{2}); B (3, 2); C (0, 1)

y = A B - A C ⩽ B C \Rightarrow y ⩽ \sqrt{{(3 - 0)}^{2} + {(2 - 1)}^{2}} = \sqrt{10}

y = \sqrt{10} \Leftrightarrow \frac{x^{2} - 1}{x - 0} = \frac{2 - 1}{3 - 0} \Leftrightarrow 3 x^{2} - x - 3 = 0 \Leftrightarrow x = \frac{1 \pm \sqrt{37}}{6}

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