If x^{6}-6 \sqrt{6} y^{6}=(x^{2}+A y^{2}) (x^{4}+B x^{2} y^{2}+C y^{4}), then what will be the value of (A^{2}-B^{2}+C^{2}) ?

SSC CHSL 10 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

Question : 66 of 100

Marks: +1, -0

x^{6}-6 √{6} y^{6}=(x^{2}+A y^{2})

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

, then what will be the value of

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

Solution:

Given,

x^{6}-6 √{6} y^{6}

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

(x^{2})^{3}-(√{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}-√{6} y^{2})(x^{4}+√{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=-√{6}, B=√{6}

\;\text " and "\; C=6

∴ (A^{2}-B^{2}+C^{2})

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

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

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