Question

if b is the mean proportional a and c , prove that a,c a²+b² and b²+c²are proportional​

Answer 1

Step-by-step explanation:

given that,

b is the mean proportional of a and c

${b }^{2} = ac$

now,

now we have to show that a, c, a^2+b^2,b^2+c^2

are in proportion.

=a^2+b^2

=a^2+ac

=a(a+c)

=b^2+c^2

=ac+c^2

=c(a+c)

a/c=a(a+c)/c(a+c)

therefore,

a, c, a2+b2,b2+c2 are in proportion.

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