Question

If 2x +3y = 8 and xy = 4 then find the value of 4x*x +9y*y

Answer 1

$\underline{ \large{ \text{Answer}}} : \\ \\ \text{We know that,} \\ { \text{a}}^{2} + { \text{b}}^{2} = { \text{(a + b)}}^{2} - \text{2ab} \\ \\ \text{Then,} \: 4 { \text{x}}^{2} + 9 { \text{y}}^{2} \\ = {\text {(2x)}}^{2} + {\text {(3y)}}^{2} \\ = { \text{(2x + 3y)}}^{2} - \text{2(2x)(3y)} \\ = { \text{(2x + 3y)}}^{2} - \text{12xy} \\ = {8}^{2} - 12 \: (4) \: \: \{ \: \because \text{2x + 3y = 8 and xy = 4 } \}\\ = 64 - 48 \\ = 16 \\ \implies \boxed{4 { \text{x}}^{2} + 9 { \text{y} }^{2} = 16} \\ \\ \bigstar \: \underline{ \large{ \text{MarkAsBrainliest}}} \: \bigstar$

Answer 2

$Hey \ there!\\\\Given,\\2x + 3y = 8\\xy = 4\\\\Squaring \ \ both\ \ sides,\\(2x+3y)^2 = 8^2\\\implies 4x^2 + 9y^2 + 2 \times 2x \times 3y = 64\\\implies 4x^2 + 9y^2 + 12xy = 64\\\implies 4x^2 + 9y^2 + 12 \times 4 = 64\\\implies 4x^2 + 9y^2 = 64 - 48\\\implies\boxed{\boxed{\bold{\huge\huge{{4x^2 + 9y^2 = 16}}}}}$