Question

if 3 X + 2 Y is equal to 12 and X Y is equal to 6 find the value of 9 X square + 4 y square​

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find the value of 9x² + 4y²

$\huge\bf\underline{Solution:-}$

$\bf\underline{\red{Given:-}}$

• 3x + 2y = 12
• xy = 6

we know that,

⇝ (a + b)² = a² + b² + 2ab

⇝ a² + b² = (a + b)² - 2ab

Then,

• Value of 9x² + 4y² is :-

Let

• a = 3x
• b = 2y

Then,

⇝ 9x² + 4y² = (3x + 2y)² - 2× 3x × 2y

we know that,

• 3x + 2y = 12
• xy = 6

Then,

⇝ 9x² + 4y² = 12² - 12 × 6

⇝9x² + 4y² = 144 - 72

⇝9x² + 4y² = 72

Hence,

• Value of 9x² + 4y² is 72

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Answer 2

Answer:56

Step-by-step explanation:As per question 3x+2y=12...........1eqn

xy=6................2eqn

9x^2+4y^2=?

From second equation we can get x =6/y

Putting the value of x in equation first

3(6/y)+2y=12

18+2y^2=12y

2y^2-12y+18=0

2y^2-6y-6y+18=0

2y(y-3)-6(y-3)=0

(2y-6)(y-3)=0

y=3,3

Putting the value of y in x=6/y

x=6/3=2

Thus putting value in equation 3

9(2)^2+4(3)^2=9*4+4*9=28+38=56