Question

If \( (a, b, c, 2 c) \) are real numbers such that \( (a)(b)(c) \neq 0 \) and given the condition: \[ \frac{b x+(1-x) c}{a}=\frac{c x+(1-x) a}{b}=\frac{a x+(1-x) b}{c} \] Then, prove that \( a=b=c \).

          If \( (a, b, c, 2 c) \) are real numbers such that \( (a)(b)(c) \neq 0 \) and given the condition:
\[
\frac{b x+(1-x) c}{a}=\frac{c x+(1-x) a}{b}=\frac{a x+(1-x) b}{c}
\]

Then, prove that \( a=b=c \).

If (a, b, c, 2 c) are real numbers such that (a)(b)(c) ≠ 0 and given the condition:

(b x+(1-x) c)/(a)=(c x+(1-x) a)/(b)=(a x+(1-x) b)/(c)

Then, prove that a=b=c.

Added by Jonathan M.

Mathematics for IIT JEE Main and Advanced Differential Calculus Algebra Trigonometry

Sanjiva Dayal IIT Kanpur 1st Edition

Chapter 10

Instant Answer

Solved by Expert Urvashi Arora

09/17/2021

Step 1

We have: \[\frac{bx + (1-x)c}{a} = \frac{cx + (1-x)a}{b} = \frac{ax + (1-x)b}{c}\] To simplify this, we can cross-multiply. Multiplying the first and second fractions, we get: \[b(bx + (1-x)c) = a(cx + (1-x)a)\] Expanding both sides, we have: \[b^2x + b(1-x)c Show more…

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