Question
Download Solution PDFIf \(\rm \frac{a+b}{b+c}=\frac{c+d}{d+a}\) a ≠ c, then which one of the following is correct ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm \frac{a+b}{b+c}=\frac{c+d}{d+a}\) a ≠ c
Concept used:
Componendo and Dividendo:
If a : b = c : d then
(a + b ) : (a – b) = (c + d) : (c – d)
Calculation:
\(\rm \frac{a+b}{b+c}=\frac{c+d}{d+a}\)According to the above concept
⇒ \(\rm \frac{a+b + b + c}{a + b - b-c}=\frac{c+d+ d + a}{c +d-d-a}\)
⇒ \(\rm \frac{a+2b + c}{a -c}=\frac{c+2d + a}{c -a}\)
⇒ \(\rm \frac{a+2b + c}{a -c}=\frac{c+2d + a}{-{(a-c)}}\)
⇒ a + 2b + c = -c - 2d - a
⇒ 2a + 2b + 2c + 2d = 0
⇒ a + b + c + d = 0
∴ The required value is a + b + c + d = 0
Last updated on May 29, 2025
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