If a : b : : c : d, then prove that 7a+11b : 7a -11b = 7c +11d : … - Vidyadip

Question

If $a : b : : c : d,$ then prove that
$7a+11b : 7a -11b = 7c +11d : 7c - 11d$

✓

Answer

$7 a+11 b: 7 a-11 b=7 c+11 d: 7 c-11 d$
$\frac{a}{b}=\frac{c}{d}$
Multiplying both sides by $\frac{7}{11}$
$\Rightarrow \frac{ a }{ b } \times \frac{7}{11}=\frac{ c }{ d } \times \frac{7}{11} $
$\Rightarrow \frac{7 a }{11 b }=\frac{7 c }{11 d }$
Applying componendo and dividendo,
$\frac{7 a +11 b }{7 a -11 b }=\frac{7 c +11 d }{7 c -11 d }$
Hence, $7 a+11 b: 7 a-11 b=7 c+11 d: 7 c-11 d$

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