62. Simplify the following expression. \;{5(a^{6}-b^{6})³+5(b^{6}-c^{6})³+5(c^{6}-a^{6})³}{2(a³-b³)³+2(b³-c³)³+2(c³-a³)³}

Correct Answer is : 52(a3+b3)(b3+c3)(c3+a3)\;5/2(a³+b³)(b³+c³)(c³+a³)25(a3+b3)(b3+c3)(c3+a3) y

\;5/2(a³+b³)(b³-c³)(c³-a³)

\;5/2(a³-b³)(b³+c³)(c³+a³)

\;5/2(a³-b³)(b³-c³)(c³+a³)

\;5/2(a³+b³)(b³+c³)(c³+a³) y

Correct Answer is : 52(a3+b3)(b3+c3)(c3+a3)\;5/2(a³+b³)(b³+c³)(c³+a³)25(a3+b3)(b3+c3)(c3+a3) y

Test Index

SSC CGL 24 Aug 2021 Shift 2 Paper

Question : 62 of 100

Marks: +1, -0

\;\frac{5(a^{6}-b^{6})^{3}+5(b^{6}-c^{6})^{3}+5(c^{6}-a^{6})^{3}}{2(a^{3}-b^{3})^{3}+2(b^{3}-c^{3})^{3}+2(c^{3}-a^{3})^{3}}

Solution:

\;\frac{5(a^{6}-b^{6})^{3}+5(b^{6}-c^{6})^{3}+5(c^{6}-a^{6})^{3}}{2(a^{3}-b^{3})^{3}+2(b^{3}-c^{3})^{3}+2(c^{3}-a^{3})^{3}}

We know that, if

a+b+c=0

then

a^{3}+b^{3}+c^{3}=3abc

So, here

a^{6}-b^{6}+b^{6}-c^{6}+c^{6}-a^{6}=0

Put

3(a^{6}-b^{6})(b^{6}-c^{6})(c^{6}-a^{6})

in place of numerator similar in denominator.

=\;\frac{5}{2}\left[\;\frac{3(a^{6}-b^{6})(b^{6}-c^{6})(c^{6}-a^{6})}{3(a^{3}-b^{3})(b^{3}-c^{3})(c^{3}-a^{3})}\right]

=\;\frac{5}{2}\left[\begin{array}{l}(a^{3}-b^{3})(a^{3}+b^{3})\times(b^{3}+c^{3})\\;\frac{(b^{3}-c^{3})\times(c^{3}+a^{3})(c^{3}-a^{3})}{(a^{3}-b^{3})(b^{3}-c^{3})(c^{3}-a^{3})}\\ [\because(a+b)(a-b)=a^{2}-b^{2}]\end{array}\right].

=\;\frac{5}{2}(a^{3}+b^{3})(b^{3}+c^{3})(c^{3}+a^{3})

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