Question

If a,b,c,d are in continuous proportion then prove that (c+a) (c+d) = (b+c) (b+d)​

Answer 1

Answer:

We must prove that (c+a)(c+d) = (b+c)(b+d)

1. Let us use principles from mathematical induction
2. $\frac{a}{b} = \frac{b}{c} = \frac{c}{d} = x$
3. a=bx , b=cx, c=dx
4. a+c = b + c
5. c +d = b + d
6. Such that (a+c)(c+d)=(b+c)(b+d)

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