Question

if 3× +4y =18 and xy =6 , find the value of 9×2 + 16y2 / 3× + 4Y = 18​

Answer 1

$\sf \pink{ \underline{\large\: Question.}}$

$\sf \: if \: \: 3x + 4y = 18 \: and \: xy = 6 \: then \: find \: the \: value \: of$

$\sf \: {\large \frac{9 {x}^{2} + 16 {y}^{2} }{3x + 4y} \: }$

$\sf \green{ \underline{\large\: solution.}}$

$\sf \: Given$

$\sf \: 3x + 4y = 18$

$\sf \: Squaring \: \: both \: \: sides$

$\sf \implies\: (3x + 4y)^{2} = (18)^{2}$

$\sf formula \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\: (a + b)^{2} = {a}^{2} + 2ab + {b}^{2}$

$\sf \implies\: (3x)^{2} + 2 \times (3x) \times (4y) + (4y)^{2} = 324$

$\sf \implies\: 9x^{2} + 24xy + 16y^{2} = 324$

$\sf \implies\: 9x^{2} + 16y^{2} = 324 - 24xy$

$\sf \: Aslo \: \: given \: \: \: xy = 6$

$\sf \implies\: 9x^{2} + 16y^{2} = 324 - 24 \times 6$

$\sf \implies\: 9x^{2} + 16y^{2} = 324 - 144$

$\sf \implies\: 9x^{2} + 16y^{2} =180 \: \: \: \: \: \: ....(i)$

Hence

$\sf \: \large \frac{9 {x}^{2} + 16 {y}^{2} }{3x + 4y} = \: \frac{180 }{18}$

$\sf \: {\large \frac{9 {x}^{2} + 16 {y}^{2} }{3x + 4y} = \:} 10 \: \: \: \: \: \: \green{ \: \leftarrow ans}$

plz mark as brainlist