Question

8. If a:b=c:d then prove that
(a) (5a +7b)(5c -7 d) =(5a-7b)(5c +7 d)
1 1 1 1
b c d 1
(b)
nb pc qd 9 p
m) Jabcd
a
+
+
+
ma
+ +
n​

Answer 1

a:b=c:d

or, a/b = c/d

or, (5/7 × a/b) = (5/7 × c/d). [by multiple 5/7 both side]

or, 5a/7b = 5c/7d

or, (5a+7b)/(5a-7b) = (5c+7d)/(5c-7d). [componendo and dividendo]

or, (5a+7b) (5c-7d) = (5c-7d) (5a+7d) [proved]

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