If a:b = b:c = c:d, prove that (a+b) = (a2+b2+c2) : (b2+c2+d2)
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To prove a 2+b 2+c 2)(b 2 +c 2 +d 2 )=(ab+bc+cd+) 2
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Substituting a,b,c
⇒((bk) 2 +(ck) 2 +(dk) 2 )(b 2 +c 2 +d 2 )=(b 2 k+c 2 k+d 2 k) 2
⇒k 2 (b2 +c 2 +d 2 )(b 2 +c 2 +d 2 )=k 2 (b 2 +c 2 +d 2 ) 2
⇒(b 2 +c 2 +d 2 ) 2 =(b 2 +c 2 +d 2 ) 2
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Hence proved.
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