Question

If 2x+3y=14 and xy=18 then 4x^2+9y^2

Answer 1

Given:-
2x+3y=14
xy=18

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$
${(2x + 3y)}^{2} = {4x}^{2} + {9y}^{2} + (2 \times 2x \times 3y)$
Here:-
${14}^{2} = {4x}^{2} + {9y}^{2} + (12 \times 18)$
$196 = {4x}^{2} + {9y}^{2} + 216$
Hence,
$-20 = {4x}^{2} + {9y}^{2}$
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