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प्रश्न
In the following, determine whether the following function is homogeneous or not. If it is so, find the degree.
h(x, y) = `(6x^3y^2 - piy^5 + 9x^4y)/(2020x^2 + 2019y^2)`
उत्तर
h(x, y) = `(6x^3y^2 - piy^5 + 9x^4y)/(2020x^2 + 2019y^2)`
`"h"(lambdax, lambday) = (6lambda^2x^2lambda^3y^3 - pilambda^5y^5 + 9lambda^4x^4lambday)/(2020lambda^2x^2 + 2019lambda^2y^2)`
= `(lambda^5(6x^2y^3 - piy^5 + 9x^4y))/(lambda^2(2020x^2 + 2019y^2))`
= `lambda^2 "h"(x, y)`
Thus f is homogeneous with degree 3.
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