Math, asked by saini0553, 1 year ago

If 3x + 2y = 12 and xy = 6, find the value of 9x^2 + 4y^2

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Answers

Answered by ravi9848267328

Answer:

Step-by-step explanation:

(3x+2y)^2=9x^2+4y^2+12xy

3x + 2y = 12 and xy = 6

144=9x^2 + 4y^2+72

9x^2 + 4y^2=72

ravi9848267328: thnx

richapariya121pe22ey: Your solution is wrong.

richapariya121pe22ey: (a+b)²=a²+2ab+b²

ravi9848267328: i did the same

ravi9848267328: u get 12xy=12(6)=72

richapariya121pe22ey: You have written 18xy. It should be 12xy.

ravi9848267328: thnx

ravi9848267328: i didnt see that

Answered by richapariya121pe22ey

3x + 2y = 12 ----- Eq 1

& xy = 6

x = 6/y ----- Eq 2

Substituting eq 2 in eq 1

3(6/y) + 2y = 12

18 + 2y² = 12y

2y² -12y + 18 = 0

y² - 6y + 9 =0

y² - 3y - 3y + 9 = 0

y(y-3)-3(y-3)=0

(y-3)(y-3)=0

y=3

Substituting y=3 in eq. 2

x=6/3=2

9x² + 4y²

=9(2)² + 4(3)²

=9(4) + 4(9)

=36 +36

=72

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