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# Algebra

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The arithmetic mean between two numbers is 75 and their geometric mean is 21. Find the numbers.

Apr 30, 2022

#1
+306
+1

Let the first number be x and the second one be y.

$$x+y\over2$$=75

$$\sqrt (xy)$$=21

(yes the xy is under the radical)

The equations can be manipulated into:

xy=441

x+y=150

From here you would have two options: graph, or solve using quadratics.

Such a graph can be found here; the intersections are (147, 3) and (3, 147), which means that the two numbers desired are 147 and 3.

You could also recognize that solving this sytem is akin to solving the quadratic x²+150x+441, which you can solve however you want to.

Apr 30, 2022

#1
+306
+1

Let the first number be x and the second one be y.

$$x+y\over2$$=75

$$\sqrt (xy)$$=21

(yes the xy is under the radical)

The equations can be manipulated into:

xy=441

x+y=150

From here you would have two options: graph, or solve using quadratics.

Such a graph can be found here; the intersections are (147, 3) and (3, 147), which means that the two numbers desired are 147 and 3.

You could also recognize that solving this sytem is akin to solving the quadratic x²+150x+441, which you can solve however you want to.

WhyamIdoingthis Apr 30, 2022
#2
+125693
0

Thx, Whyamidoingthis   !!!!

Nice solution.....

CPhill  Apr 30, 2022