Question

If b is the mean proportion between a & c,show that b(a+c)is the mean proportion between (a*a+b*b)&(b*b+c*c)

Answer 1

Correct question : If b is the mean proportional between a and c, prove that ( ab + bc ) is mean proportional of (a 2+b 2) and (b 2+c 2) .

Solution : Given : b is the mean proportional between a and c , So

b2 = ac

Now (a 2+b 2)(b 2+c 2) = (a 2+ ac )( ac +c 2) ,

(a 2+b 2)(b 2+c 2) = a(a + c ) c( a + c ) ,

(a 2+b 2)(b 2+c 2) = a c (a + c )2 ,

(a 2+b 2)(b 2+c 2) = b2 (a + c )2

(a 2+b 2)(b 2+c 2) = (ab + bc )2

So,
( ab + bc ) is mean proportional of (a 2+b 2) and (b 2+c 2) . ( Hence proved )

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