If the sum of three numbers in G.P. is $$63$$ and the product of the first and the second term is $$34of$$ the third term, then the numbers are

Question

If the sum of three numbers in G.P. is $$63$$ and the product of the first and the second term is $$34of$$ the third term, then the numbers are

Infinity Learn · Accepted Answer

Let the three numbers be a, ar,$$ar2Given$$ $$a+ar+ar2=63--------------$$ (1)and$$ a⋅$$ar=34$$⋅$$ar2$$ or $$a=34r------------------(2)putting$$ in  $$(1)   $$34r+34r$$⋅$$r+34r$$⋅$$r2=63or$$          $$r3+r2+r$$−$$84=0$$ or  (r$$−$$4)r2+5r+21=0$$∴ $$r=4$$,−$$5$$±$$25$$−$$842$$∴ Real value of r is $$4$$. Putting this value in $$(2),   $$a=34$$×$$4=3$$∴The three numbers are $$3$$,$$3$$×$$4$$,$$3$$×$$42$$,i e  $$3$$, $$12$$, $$48$$.

If the sum of three numbers in G.P. is 63 and the product of the first and the second term is $\frac{3}{4}$ of the third term, then the numbers are

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If the sum of three numbers in G.P. is 63 and the product of the first and the second term is 34of the third term, then the numbers are

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If the sum of three numbers in G.P. is 63 and the product of the first and the second term is $\frac{3}{4}$ of the third term, then the numbers are