b(32v2)k 3-22Example 7. IfA and G be A.M. and G.M. respectively betuep

1.	b(32v2)k 3-22Example 7. IfA and G be A.M. and G.M. respectively betuep ,(A + G)(A-G)rove that the numbers areA t
Answer» If A and G be A.M and G.m, respectively between 2 positive numbers, prove that one of the numbers is => A ± √[ A² - G² ] Soln : Let x and y be the two numbers. Then -- ....... x + y = 2A .......... (1) and xy = G² ......... (2) From (2) we get -- => x = G²/y . Substitute this value of x in eqn (1). We get --- ( G²/y ) + y = 2A => G² + y² - 2 A y = 0 => y² - 2 A y + G² = 0 . this is a quadratic eqn in y . Hence 2 A ± √[ 4 A² - 4 G² ] => y = A ± √[ A² - G² ] => y = A ± √[ ( A + G ) ( A - G ) ] Like my answer if you find it useful!

b(32v2)k 3-22Example 7. IfA and G be A.M. and G.M. respectively betuep ,(A + G)(A-G)rove that the numbers areA t

Answer»

If A and G be A.M and G.m, respectively between 2 positive numbers, prove that one of the numbers is

=> A ± √[ A² - G² ]

Soln : Let x and y be the two numbers. Then --

....... x + y = 2A .......... (1) and xy = G² ......... (2)

From (2) we get --

=> x = G²/y . Substitute this value of x in eqn (1). We get ---

( G²/y ) + y = 2A

=> G² + y² - 2 A y = 0

=> y² - 2 A y + G² = 0 . this is a quadratic eqn in y . Hence

2 A ± √[ 4 A² - 4 G² ]

=> y = A ± √[ A² - G² ]

=> y = A ± √[ ( A + G ) ( A - G ) ]

Like my answer if you find it useful!