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$If a, b, c are real numbers, then the intervals in which$ $f (x) = |\begin{matrix} x + a^{2} & a b & a c \\ a b & x + b^{2} & b c \\ a c & b c & x + c^{2} \end{matrix}| is strictly decreasing$

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a

x < 0

b

x > 0

c

0 < x < 1

d

[−23, 0]

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detailed solution

Correct option is D

f(x)=1abcax+a2ab2ac2a2bbx+b2bc2a2cb2ccx+c2=abcabcx+a2b2c2a2x+b2c2a2b2x+c2=x+a2+b2+c2b2c2x+a2+b2+c2x+b2c2x+a2+b2+c2b2x+c2=x+a2+b2+c21b2c21x+b2c21b2x+c2=x2x+a2+b2+c2f′(x)=3x2+2xa2+b2+c2f′(x)<0x(3x+2)a2+b2+c2≤0−23a2+b2+c2≤x≤0x(3x+2)≤0−23≤x≤0

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Similar Questions

If a, b, c are real numbers, then the intervals in which $f (x) = |\begin{array}{l} x + a^{2} a b a c \\ a b x + b^{2} b c \\ a c b c x + c^{2} \end{array}| is strictly decreasing$

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