Let $a, b, c, x, y, z$ be positive real numbers such that $a + b + c = x + y + z$ and $a b c = x y z .$ Further, suppose that $a \leq x < y < z \leq c$ and $a < b < c .$ then $a = x, b = y,$ and $c = z$

True

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False

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Solution

The correct option is A True

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Let a,b,c,x,y,z be positive real numbers such that a+b+c=x+y+z and abc=xyz. Further, suppose that a≤x<y<z≤c and a<b<c. then a=x,b=y, and c=z

The correct option is A True

Let $a, b, c, x, y, z$ be positive real numbers such that $a + b + c = x + y + z$ and $a b c = x y z .$ Further, suppose that $a \leq x < y < z \leq c$ and $a < b < c .$ then $a = x, b = y,$ and $c = z$