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SSC CHSL 10 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 66 of 100

Marks: +1, -0

x^{6}-6 \sqrt{6} y^{6}=(x^{2}+A y^{2})

(x^{4}+B x^{2} y^{2}+C y^{4})

(A^{2}-B^{2}+C^{2})

Solution:

Given,

x^{6}-6 \sqrt{6} y^{6}

\\;\\;\\; =(x^{2}+A y^{2})(x^{4}+B x^{2} y^{2}+C y^{4})

(x^{2})^{3}-(\sqrt{6} y^{2})^{3}

\\;\\;\\; =(x^{2}+A y^{2})(x^{4}+B x^{2} y^{2}+C y^{4})

\\;\text{ Since, }\\; a^{3}-b^{3}=(a-b)(a^{2}+a b+b^{2})

(x^{2}-\sqrt{6} y^{2})(x^{4}+\sqrt{6} x^{2} y^{2}+6 y^{4})

\\;\\;\\; =(x^{2}+A y^{2})(x^{4}+B x^{2} y^{2}+C y^{4})

On comparison of both sides,

\\;\\;\\; A=-\sqrt{6}, B=\sqrt{6}

\\;\text{ and }\\; C=6

\therefore (A^{2}-B^{2}+C^{2})

\\;\\;\\; =(-\sqrt{6})^{2}-(\sqrt{6})^{2}+(6)^{2}

\\;\\;\\; =6-6+36=36

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