Find two numbers whose A.M exceeds their G.M by 1/2 and their H.M by 25/26
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Let the two numbers be a and b
The A.M of the numbers is given by the formula (a+b)÷2
The G.M of the numbers is given by the formula √a×b
The H.M of the numbers is given by the formula 2÷((1÷a)+(1÷b))
A.M exceeds G.M by 1/2
(a+b)÷2 +(1÷2)= √a×b
(a+b+1) ÷2= √a×b
A.M exceeds H.M by 25/26
(a+b)÷2 +(25÷26) = 2×a×b ÷(a+b)
(13a + 13b +25)÷ 26= 2ab÷(a+b)
We have two equations and have two variables we can solve the equations and we can obtain the value of a and b
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