If [tex]3x + 2y = 12[/tex] and [tex]xy = 6[/tex], then find the value of [tex]9x^{2} + 4y^{2}[/tex].

xy=6 x=6/y......1 3x+2y=12 from1 3*(6/y)+2y=12 {after solving}2y^2-12y+18=0 y^2-6y+9=0 {taking y common} y^2-3y-3y+9=0 y(y-3)-3(y-3)=0 y=3,3............2 putting 2 in 1 x=2.........3
9x^2+4y^2= from 2 and 3 9 4+4 9=36+36= 72

Answered by vaibhavay | 2024-06-10

3 x + 2 y = 12 ( 3 x + 2 y ) 2 = 144 9 x 2 + 12 x y + 4 y 2 = 144 9 x 2 + 4 y 2 = 144 − 12 x y 9 x 2 + 4 y 2 = 144 − 12 ⋅ 6 9 x 2 + 4 y 2 = 144 − 72 9 x 2 + 4 y 2 = 72 ​

Answered by konrad509 | 2024-06-10

The value of 9 x 2 + 4 y 2 is 72 , found by solving the system of equations 3 x + 2 y = 12 and x y = 6 . We substituted one variable into the other, solved for the variable values, and calculated the resulting expression. In total, we found that x = 2 and y = 3 .
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Answered by vaibhavay | 2025-06-12