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the sum of three of a g.p. is 21 and the sum of their squares is 189. find the numbers.
\n" ); document.write( "let three terms are a,b,c in GP
\n" ); document.write( "as per given conditions
\n" ); document.write( "a+b+c =21(1)
\n" ); document.write( "a+c=21-b
\n" ); document.write( "a^2 + b^2 + C^2 = 189(2)
\n" ); document.write( "by using formula
\n" ); document.write( "(a+b+C)^2= a^2 + b^2 +c^2 + 2ab +2bc+2ca by substituting the value from (1) and (2)
\n" ); document.write( "(21)^2= 189+2(ab +bc +ca )
\n" ); document.write( "441 =189 +2(ab +bc +ca )
\n" ); document.write( "441-189 /2= ab + bc +ca
\n" ); document.write( "252/2 =ab+bc +ca
\n" ); document.write( "126= ab +bc +ca we know if a,b,c are in GP than b^2=ac
\n" ); document.write( "126=ab +bc +b^2
\n" ); document.write( "126=b(a+c) +b^2 by putting a+c=21-b from (1)
\n" ); document.write( "126=b(21-b) +b^2
\n" ); document.write( "126= 21b -b^2 +b^2
\n" ); document.write( "126=21b
\n" ); document.write( "126/21 =b
\n" ); document.write( "b=6
\n" ); document.write( "a+c=21-b
\n" ); document.write( "a+c=21-6 =15
\n" ); document.write( "both a and c are in GP than a=3 and c=12
\n" ); document.write( "therefore
\n" ); document.write( "Answer a=3 b=6 c= 12 \r
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