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if (x+2y) ² =x² + pxy +4y² , then the value of p is ________​

By Margaret

if (x+2y) ² =x² + pxy +4y² , then the value of p is ________​

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Margaret

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2 thoughts on “if (x+2y) ² =x² + pxy +4y² , then the value of p is ________​”

  2. If x^2+4y^2=40 ……………(i) and xy=6

    If xy=6 Therefore, x=6/y

    Put x=6/y in (i)

    (6/y)^2+4y^2=40

    36/y^2+4y^2=40

    (36+4y^4)/y^2=40

    36+4y^4=40y^2 …………..(ii)

    Let y^2=z

    therefore, equation (ii) becomes

    36+4z^2=40z ………. (iii)

    Divide (iii) by 4 it becomes

    9+z^2=10z

    z^2–10z+9=0……………(iv)

    z^2-z-9z+9=0

    z(z-1)-9(z-1)=0

    (z-1)(z-9)=0

    Hence, Z=1 or 9

    Taking Z=1, We have

    y^2=1

    y=1

    Taking Z=9, we have

    y^2=9

    y=3

    Putting y=1 in equation (i), we have

    x^2+4(1)^2=40

    x^2+4=40

    x^2=36

    x=6

    Therefore, x+2y= 6+2(1)=6+2=8

    Putting y=3 in equation (i) we have,

    x^2+4(3)^2=40

    x^2+4(9)=40

    x^2=40–36

    x^2=4

    x=2

    Therefore, x+2y= 2+2(3)=2+6=8

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