Question

If x2 +9y2= 9 and xy =1 find ( 2x+6y)2

Answer 1

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Answer 2

Given,

x² + 9y² = 9 and  xy = 1

$x^{2}+9y^{2}=9\\\\x^{2}+(3y)^{2}=9\\\\x^{2}+(3y)^{2}+2\times x\times3y-6xy=9\\\\(x+3y)^{2}-6xy=9\\ \\(x+3y)^{2}-6\times 1=9\\\\(x+3y)^{2}-6=9\\ \\(x+3y)^{2}=15\\ \\x+3y=\frac{+}{}\sqrt{15}\\\\2x+6y=\frac{+}{}2\sqrt{15}\\\\2(2x+6y)=\frac{+}{}4\sqrt{15}$