Question

If 2x+3y=13 and xy =6 then 4x²+9x²​

Answer 1

Step 1

(2x+3y)^2 =4x^2+9x+2*2x*3y

Step 2

13^2=4x^2+9y^2+12*6

Step 3

169-12*6=4x^2+9y^2

Step 4

169-72= 4x^2+9y^2

Step 5

4x^2+9y^2=97

Answer 2

Answer:

52 or 13

Step-by-step explanation:

$y = \frac{6}{x}$

$2x + 3( \frac{6}{x} ) = 13$

$2 {x}^{2} + 18 = 13x$

$2 {x}^{2} - 13x + 18 = 0$

$2 {x}^{2} - 4x - 9x + 18 = 0$

$2x(x - 2) - 1(x - 2) = 0$

$(2x - 2)(x - 2) = 0$

$x = 2 \: or \: x = 1$

$4 {x}^{2} + 9 {x }^{2} = 4(4) + 9(4) \\ = 52 \\ 4(1) + 9(1) = 13$