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Question 19
If $$5\sqrt{5}x^3 + 2\sqrt{2}y^3 = (Ax + \sqrt{2}y)(Bx^2 + 2y^2 + Cxy)$$, then the value of $$(A^2 + B^2 - C^2 )$$ is:
Solution
$$5\sqrt{5}x^3 + 2\sqrt{2}y^3 = (Ax + \sqrt{2}y)(Bx^2 + 2y^2 + Cxy)$$
$$(\sqrt{5}x +Â \sqrt{2}y)(5x^2 + 2y^2 +Â \sqrt{10}xy) = (Ax + \sqrt{2}y)(Bx^2 + 2y^2 + Cxy)$$Â
On comparing,
A =Â $$\sqrt{5}$$
B = 5
C =Â $$\sqrt{10}$$
$$(A^2 + B^2 - C^2 )$$
=Â $$((\sqrt{5})^2 + 5^2 - (\sqrt{10})^2 )$$
= 5 +Â 25 - 10 = 20
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