compute the value of 9 X square + 4 y square if X Y is equal to 6 and 3 X + 2 Y is equal to 12
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compute the value of 9 X square + 4 y square if X Y is equal to 6 and 3 X + 2 Y is equal to 12
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Answer:
(a+b)^2 = a^2+ b^2+2ab
Therefore (3x+2y)^2 = 9x^2 + 4y^2 + 2xy .
= 16 + 12
= 28.
Step-by-step explanation:
[tex]\sf\large\underline{Question:}[/tex]
Compute the value of 9x²+4y². If xy=6 and 3x+2y=12
[tex]\sf\large\underline{Given:}[/tex]
[tex]\sf\large\underline{To\: Find:}[/tex]
[tex]\sf\large\underline{Solution:}[/tex]
[tex]\rm{\implies xy=6}[/tex]
[tex]\rm{\implies x=\dfrac{6}{y}}[/tex]
[tex]\rm{\implies 3x+2y=12}[/tex]
[tex]\rm{\implies 3(\dfrac{6}{y})+2y=12}[/tex]
[tex]\rm{\implies \dfrac{18}{y}+2y=12}[/tex]
[tex]\rm{\implies \dfrac{18+2y^2}{y}=12}[/tex]
[tex]\rm{\implies 2y^2+18=12y}[/tex]
[tex]\rm{\implies 2y^2-12y+18=0}[/tex]
[tex]\rm{\implies y^2-6y+9=0}[/tex]
[tex]\rm{\implies y^2-3y-3y+9=0}[/tex]
[tex]\rm{\implies y(y-3)-3(y-3)=0}[/tex]
[tex]\rm{\implies (y-3)(y-3)=0}[/tex]
[tex]\rm{\implies \therefore y=3}[/tex]
[tex]\rm{\implies xy=6}[/tex]
[tex]\rm{\implies 3x=6}[/tex]
[tex]\rm\red{\implies x=2}[/tex]
[tex]\rm{\implies 9x^2+4y^2}[/tex]
[tex]\rm{\implies 9(2)^2+4(3)^2}[/tex]
[tex]\rm{\implies 9*4+4*9}[/tex]
[tex]\rm{\implies 36+36}[/tex]
[tex]\rm{\implies 72}[/tex]
Hence,
[tex]\rm\purple{\implies The\: value\:of\:9x^2+4y^2=72}[/tex]