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

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

Themaximumvalueofy=(x−3)2+(x2−2)2−x2+(x2−1)2is(A)10(C)4(B)25(D)10

Answered by mitica last updated on 20/Jun/21

(A) (√(10))

(A)10

Answered by mitica last updated on 20/Jun/21

A(x,x^2 );B(3,2);C(0,1) y=AB−AC≤BC⇒y≤(√((3−0)^2 +(2−1)^2 ))=(√(10)) y=(√(10))⇔((x^2 −1)/(x−0))=((2−1)/(3−0))⇔3x^2 −x−3=0⇔x=((1±(√(37)))/6)

A(x,x2);B(3,2);C(0,1)y=AB−AC⩽BC⇒y⩽(3−0)2+(2−1)2=10y=10⇔x2−1x−0=2−13−0⇔3x2−x−3=0⇔x=1±376

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