Question

The sum of two numbers is 45 and the mean proportional betweem them is 18.the numbers are

Answer 1

x = first number

y = second number


x + y = 45 Subtract x to both sides

x + y - x = 45 - x

y = 45 - x


square root ( x * y ) = 18 Take square of both sides

x * y = 18 ^ 2

x * y = 324

x * ( 45 - x ) = 324

x * 45 - x * x = 324

45 x - x ^ 2 = 324 Subtract 324 to both sides

45 x - x ^ 2 - 324 = 324 - 324

45 x - x ^ 2 - 324 = 0

- x ^ 2 + 45 x - 324 = 0 Multiply by - 1

x ^ 2 - 45 x + 324 = 0


The solutions are :

x = 9 and x = 36


For x = 9

y = 45 - x = 45 - 9 = 36


For x = 36

y = 45 - x = 45 - 36 = 9

So numbers are 9 and 36

9 + 36 = 45

square root ( 9 * 36 ) = square root ( 324 ) = 18


P.S

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x ^ 2 - 45 x + 324 = 0

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x ^ 2 - 45 x + 324 = 0

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