If x+y=12 and xy=27,find the value of x^2+y^2
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x=9or3 y=3or9
Step-by-step explanation:
x+y=12
x=27/y
27/y+y=12
27+y^2/y=12
27+y^2=12y
we get a quadratic equation
y^2-12y+27=0
y^2-9y-3y+27=0
y(y-9)-3(y-9)=0
(y-3)(y-9)=0
y=3 or y=9
x×3=27
x=9
x×9=27
x=3
Answered by
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Step-by-step explanation:
Given x+y=12 and xy=27
Now, squaring on both sides,we get
- (x+y)^2=12^2
we know that (a+b)^2=a^2+2ab+b^2
- x^2+2xy+y^2=144
but we have xy=27
- x^2+y^2+2(27)=144
- x^2+y^2+54=144
- x^2+y^2=144-54
- x^2+y^2=90
- The value of x^2+y^2=90
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