Q54 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Mathematics

If $a, b, c$ are distinct positive real numbers and $a^2+b^2+c^2=1$, then the value of $a b+b c+c a$ is

  • Correct answer
    A
    less than 1
  • B
    greater than 1
  • C
    equals to 1
  • D
    any real number

Solution

Given, $a, b$ and $c$ are positive distinct real number. Also, $a^2+b^2+c^2=1$ As square of a number is also positive, so $\begin{aligned} & 0 < a^2, b^2, c^2 < 1 \\ & \Rightarrow 0 < a, b, c, < 1 \end{aligned}$ $\therefore$ Values of $a b+b c+c a$ is less than one.

Hence, the correct answer is option: 'A'.

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