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Integration of Irrational Algebraic Fractions - 1

If 𝑚=9𝑥2−4�...

Question

If $m = 9 x^{2} - 4 x y + 5 y^{2}$ and $n = - 3 x^{2} + 2 x y - y^{2},$
find: (i) 2𝑚−𝑛

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Solution

Step: Putting the value of m and n in required equation $m = 9 x^{2} - 4 x y + 5 y^{2}$
Then $2 m = 2 [9 x^{2} - 4 x y + 5 y^{2}]$
$= 18 x^{2} - 8 x y + 10 y^{2}$ and $n = - 3 x^{2} + 2 x y - y^{2}$
$\Rightarrow 2 m - n$ $= 18 x^{2} - 8 x y + 10 y^{2} - (- 3 x^{2} + 2 x y - y^{2})$ $= 18 x^{2} - 8 x y + 10 y^{2} + 3 x^{2} - 2 x y + y^{2}$ $= 18 x^{2} + 3 x^{2} - 8 x y - 2 x y + 10 y^{2} + y^{2}$ $= 21 x^{2} - 10 x y + 11 y^{2}$
Hence, the answer is $21 x^{2} - 10 x y + 11 y^{2} .$

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Integration of Irrational Algebraic Fractions - 1

Standard XII Mathematics

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