the sum of two numbers is 25 and their product is 144. find the numbers

Question

the sum of two numbers is 25 and their product is 144. find the numbers

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Serenity 5 days 2021-09-14T01:49:05+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-14T01:50:23+00:00

    Answer:

    Let

    One number = x

    other number = y

    Sum

    ====

    x+y=25

    x=25-y……………(1)

    Product

    =======

    xy=144……………(2)

    Put the value of x in above equation

    (25-y)y=144

    25y-y^2=144

    y^2-25y+144=0

    y^2-16y-9y+144=0

    y^2-16y-9y+144=0

    y(y-16)-9(y-16)=0

    (y-9)(y-16)=0

    y-9=0 or y-16=0

    y=9 or y=16

    Put the value of y in (1)

    x=25-16=9

    x=25-9=16

    So numbers are 9 and 16

    0
    2021-09-14T01:51:03+00:00

    ✍ What Is Given ?

    • The sum of two numbers is 25.
    • Their product is 144.

    ✍ What we need to find ?

    • The 2 numbers.

    ✍ Solution :-

    Let one number be x.

    Let another number be y.

    So, As per Equation,

    x + y = 25,

    x × y = 144.

    \sf{x + y = 25}

    \sf{y = 25 - x}

    Now, xy = 144. __________(eq. 1)

    Put the value of x.

    \sf{y(25 - y) = 144}

    \sf{25y  -  {y}^{2}  = 144}

    We Can Write It As,

    \sf{ {y}^{2}  - 25y  - 144 = 0}

    Use Splitting Middle Term Method.

    \sf{ {y}^{2}  - 16y - 9y  - 144 = 0}

    Take Common.

    \sf{y(y - 16) - 9(y - 16) = 0 }

    \sf{(y - 9)(y - 16) = 0}

    So, Y = 9 Or 16,

    Put the values Of Y in (eq. 1)

    xy = 144

    9x = 144

    x = 16.

    So, Your Numbers Are 9 and 16.

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