Question

10. If b is the mean proportional between a and c
prove that a, c, a^2 + b^2 and b^2
+ c ^2 are porportional
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Answer 1

Let a,b,c are in proportion => b^2 = ac

=>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)

=> a , c , a(a + c) , c(a + c) are in proportion

=> a , c , a^2 + b^2 , b^2 + c^2 are in proportion.

since b is the mean proportion b/w a and c

therefore b^2=ac

a/c=(a^2+b^2)/(b^2+c^2)=(a^2+ac)/(c^2+ac)

=a/c

Hope it helps u...✌️❣️