AP EAMCET · Maths · Basic of 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
- A less than 1
- B greater than 1
- C equals to 1
- D any real number
Answer & Solution
Correct Answer
(A) less than 1
Step-by-step Solution
Detailed explanation
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.
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